Abstract group data - 17496.ro

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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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 4, 24, 4, 6, 6], 'aut_gens': [[1, 2, 24, 72, 216, 648, 1944, 5832], [14641, 11782, 14736, 10296, 17136, 1296, 14160, 11664], [15097, 10718, 10512, 17328, 600, 6480, 8688, 11664], [2229, 1082, 3768, 7824, 7248, 12960, 16896, 5832], [645, 4654, 13416, 2976, 12792, 6480, 15000, 11664], [2317, 7654, 24, 1272, 13176, 1296, 15984, 11664], [7381, 10450, 14040, 1368, 15672, 1296, 11088, 11664]], 'aut_group': None, 'aut_hash': 1698888457896312528, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 93312, 'aut_permdeg': 972, 'aut_perms': 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'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [3, 24, 2, 1], [3, 24, 4, 2], [3, 24, 8, 1], [3, 72, 2, 2], [3, 72, 4, 3], [3, 72, 8, 1], [4, 486, 1, 2], [4, 1458, 1, 1], [6, 81, 2, 1], [6, 162, 1, 2], [6, 162, 2, 2], [6, 324, 1, 1], [6, 324, 2, 1], [12, 486, 2, 4], [12, 486, 4, 2], [12, 1458, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times C_3^3:C_3^2.D_4.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 1698888457896312528, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times C_3^3:C_3^2.D_4.C_2^3', 'cc_stats': [[1, 1, 1], [2, 81, 1], [3, 1, 2], [3, 2, 6], [3, 4, 3], [3, 24, 18], [3, 72, 24], [4, 486, 2], [4, 1458, 1], [6, 81, 2], [6, 162, 6], [6, 324, 3], [12, 486, 16], [12, 1458, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': None, 'commutator_count': 2, 'commutator_label': None, 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 457, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [3, 24, 1, 2], [3, 24, 2, 8], [3, 72, 1, 8], [3, 72, 2, 8], [4, 486, 1, 2], [4, 1458, 1, 1], [6, 81, 2, 1], [6, 162, 1, 2], [6, 162, 2, 2], [6, 324, 1, 1], [6, 324, 2, 1], [12, 486, 2, 4], [12, 486, 4, 2], [12, 1458, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 486, 'exponent': 12, 'exponents_of_order': [7, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [24, 0, 8]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '1944.3931', 'hash': 6736393944771584879, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [12, 12, 3, 3, 3, 3, 3, 3], 'inner_gens': [[1, 10102, 15336, 312, 10488, 648, 16296, 5832], [4253, 2, 13944, 3840, 1200, 6480, 13056, 11664], [11257, 5162, 24, 1368, 216, 648, 2592, 5832], [1777, 4946, 672, 72, 7344, 648, 8424, 5832], [8809, 12914, 24, 12384, 216, 648, 2592, 5832], [1, 11666, 24, 72, 216, 648, 1944, 5832], [5377, 7970, 1320, 13032, 1512, 648, 1944, 5832], [1, 11666, 24, 72, 216, 648, 1944, 5832]], 'inner_hash': 745905227323407307, 'inner_nilpotent': False, 'inner_order': 5832, 'inner_split': False, 'inner_tex': 'C_3.C_3^5.Q_8', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 5], [6, 8], [8, 30], [9, 8], [12, 4], [18, 14], [24, 12], [36, 2]], 'label': '17496.ro', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'He3^2:C4.S3', 'ngens': 10, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 87, 'number_divisions': 52, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 790, 'number_subgroup_classes': 2926, 'number_subgroups': 117378, 'old_label': None, 'order': 17496, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 81], [3, 2186], [4, 2430], [6, 2106], [12, 10692]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 9300, 9300], 'outer_gens': [[5833, 13618, 10512, 14304, 14664, 6480, 11016, 11664], [1, 8326, 13416, 12384, 12096, 12960, 16584, 5832], [1, 6994, 15336, 9456, 1680, 648, 7488, 5832], [1, 12170, 15336, 9456, 1680, 648, 7488, 5832]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [121, 414, 1, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 1], [8, 10], [12, 2], [16, 10], [18, 6], [24, 3], [36, 6], [48, 6], [72, 1]], 'representations': {'PC': {'code': '112388091226561653903773178072761083887788946493827994777422107734327960213355914734598896703378840623614525709730488786047', 'gens': [1, 2, 5, 6, 7, 8, 9, 10], 'pres': [10, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 34680, 202041, 51, 48122, 82, 493123, 766804, 348614, 16824, 18725, 115215, 196585, 3465, 734166, 42016, 109646, 7196, 259217, 1466648, 587538, 87508, 9768, 10588, 1148, 583219]}, 'Perm': {'d': 36, 'gens': [42545803346368687094094289976978112054214, 319118152942818097970877275827683845520000]}}, 'schur_multiplier': [3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\He_3^2:C_4.S_3', '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: 153396903
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 457, 'group_order': 17496, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 153396914
    {'aut_label': '2A', 'centralizer': '81.a1', 'counter': 2, 'group_counter': 457, 'group_order': 17496, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 12108, 'size': 81}
  • id: 153396925
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 457, 'group_order': 17496, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 7128, 'size': 1}
  • id: 153396936
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 457, 'group_order': 17496, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 12312, 'size': 1}
  • id: 153396947
    {'aut_label': '3B', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 457, 'group_order': 17496, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 5832, 'size': 2}
  • id: 153396958
    {'aut_label': '3C', 'centralizer': '2.b1', 'counter': 6, 'group_counter': 457, 'group_order': 17496, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 7144, 'size': 2}
  • id: 153396969
    {'aut_label': '3D1', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 457, 'group_order': 17496, 'label': '3D1', 'order': 3, 'powers': [8, 1], 'representative': 6480, 'size': 2}
  • id: 153396980
    {'aut_label': '3D1', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 457, 'group_order': 17496, 'label': '3D-1', 'order': 3, 'powers': [7, 1], 'representative': 12960, 'size': 2}
  • id: 153396989
    {'aut_label': '3E1', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 457, 'group_order': 17496, 'label': '3E1', 'order': 3, 'powers': [10, 1], 'representative': 16, 'size': 2}
  • id: 153396904
    {'aut_label': '3E1', 'centralizer': '2.b1', 'counter': 10, 'group_counter': 457, 'group_order': 17496, 'label': '3E-1', 'order': 3, 'powers': [9, 1], 'representative': 8, 'size': 2}
  • id: 153396905
    {'aut_label': '3F', 'centralizer': '4.a1', 'counter': 11, 'group_counter': 457, 'group_order': 17496, 'label': '3F', 'order': 3, 'powers': [11, 1], 'representative': 6488, 'size': 4}
  • id: 153396906
    {'aut_label': '3G1', 'centralizer': '4.a1', 'counter': 12, 'group_counter': 457, 'group_order': 17496, 'label': '3G1', 'order': 3, 'powers': [13, 1], 'representative': 11680, 'size': 4}
  • id: 153396907
    {'aut_label': '3G1', 'centralizer': '4.a1', 'counter': 13, 'group_counter': 457, 'group_order': 17496, 'label': '3G-1', 'order': 3, 'powers': [12, 1], 'representative': 5840, 'size': 4}
  • id: 153396908
    {'aut_label': '3H', 'centralizer': '24.e1', 'counter': 14, 'group_counter': 457, 'group_order': 17496, 'label': '3H', 'order': 3, 'powers': [14, 1], 'representative': 24, 'size': 24}
  • id: 153396909
    {'aut_label': '3H', 'centralizer': '24.e1', 'counter': 15, 'group_counter': 457, 'group_order': 17496, 'label': '3I', 'order': 3, 'powers': [15, 1], 'representative': 2016, 'size': 24}
  • id: 153396910
    {'aut_label': '3J1', 'centralizer': '24.e1', 'counter': 16, 'group_counter': 457, 'group_order': 17496, 'label': '3J1', 'order': 3, 'powers': [17, 1], 'representative': 5856, 'size': 24}
  • id: 153396911
    {'aut_label': '3J1', 'centralizer': '24.e1', 'counter': 17, 'group_counter': 457, 'group_order': 17496, 'label': '3J-1', 'order': 3, 'powers': [16, 1], 'representative': 4104, 'size': 24}
  • id: 153396912
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 18, 'group_counter': 457, 'group_order': 17496, 'label': '3K1', 'order': 3, 'powers': [19, 1], 'representative': 32, 'size': 24}
  • id: 153396913
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 19, 'group_counter': 457, 'group_order': 17496, 'label': '3K-1', 'order': 3, 'powers': [18, 1], 'representative': 40, 'size': 24}
  • id: 153396915
    {'aut_label': '3J1', 'centralizer': '24.e1', 'counter': 20, 'group_counter': 457, 'group_order': 17496, 'label': '3L1', 'order': 3, 'powers': [21, 1], 'representative': 7848, 'size': 24}
  • id: 153396916
    {'aut_label': '3J1', 'centralizer': '24.e1', 'counter': 21, 'group_counter': 457, 'group_order': 17496, 'label': '3L-1', 'order': 3, 'powers': [20, 1], 'representative': 2664, 'size': 24}
  • id: 153396917
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 22, 'group_counter': 457, 'group_order': 17496, 'label': '3M1', 'order': 3, 'powers': [23, 1], 'representative': 2024, 'size': 24}
  • id: 153396918
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 23, 'group_counter': 457, 'group_order': 17496, 'label': '3M-1', 'order': 3, 'powers': [22, 1], 'representative': 2032, 'size': 24}
  • id: 153396919
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 24, 'group_counter': 457, 'group_order': 17496, 'label': '3N1', 'order': 3, 'powers': [25, 1], 'representative': 5864, 'size': 24}
  • id: 153396920
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 25, 'group_counter': 457, 'group_order': 17496, 'label': '3N-1', 'order': 3, 'powers': [24, 1], 'representative': 464, 'size': 24}
  • id: 153396921
    {'aut_label': '3O1', 'centralizer': '24.e1', 'counter': 26, 'group_counter': 457, 'group_order': 17496, 'label': '3O1', 'order': 3, 'powers': [27, 1], 'representative': 4112, 'size': 24}
  • id: 153396922
    {'aut_label': '3O1', 'centralizer': '24.e1', 'counter': 27, 'group_counter': 457, 'group_order': 17496, 'label': '3O-1', 'order': 3, 'powers': [26, 1], 'representative': 11696, 'size': 24}
  • id: 153396923
    {'aut_label': '3O1', 'centralizer': '24.e1', 'counter': 28, 'group_counter': 457, 'group_order': 17496, 'label': '3P1', 'order': 3, 'powers': [29, 1], 'representative': 7856, 'size': 24}
  • id: 153396924
    {'aut_label': '3O1', 'centralizer': '24.e1', 'counter': 29, 'group_counter': 457, 'group_order': 17496, 'label': '3P-1', 'order': 3, 'powers': [28, 1], 'representative': 2680, 'size': 24}
  • id: 153396926
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 30, 'group_counter': 457, 'group_order': 17496, 'label': '3Q1', 'order': 3, 'powers': [31, 1], 'representative': 2672, 'size': 24}
  • id: 153396927
    {'aut_label': '3K1', 'centralizer': '24.e1', 'counter': 31, 'group_counter': 457, 'group_order': 17496, 'label': '3Q-1', 'order': 3, 'powers': [30, 1], 'representative': 7864, 'size': 24}
  • id: 153396928
    {'aut_label': '3R', 'centralizer': '72.e1', 'counter': 32, 'group_counter': 457, 'group_order': 17496, 'label': '3R', 'order': 3, 'powers': [32, 1], 'representative': 1944, 'size': 72}
  • id: 153396929
    {'aut_label': '3S', 'centralizer': '72.f1', 'counter': 33, 'group_counter': 457, 'group_order': 17496, 'label': '3S', 'order': 3, 'powers': [33, 1], 'representative': 216, 'size': 72}
  • id: 153396930
    {'aut_label': '3T', 'centralizer': '72.g1', 'counter': 34, 'group_counter': 457, 'group_order': 17496, 'label': '3T', 'order': 3, 'powers': [34, 1], 'representative': 72, 'size': 72}
  • id: 153396931
    {'aut_label': '3R', 'centralizer': '72.e1', 'counter': 35, 'group_counter': 457, 'group_order': 17496, 'label': '3U', 'order': 3, 'powers': [35, 1], 'representative': 2160, 'size': 72}
  • id: 153396932
    {'aut_label': '3R', 'centralizer': '72.e1', 'counter': 36, 'group_counter': 457, 'group_order': 17496, 'label': '3V', 'order': 3, 'powers': [36, 1], 'representative': 1968, 'size': 72}
  • id: 153396933
    {'aut_label': '3R', 'centralizer': '72.e1', 'counter': 37, 'group_counter': 457, 'group_order': 17496, 'label': '3W', 'order': 3, 'powers': [37, 1], 'representative': 504, 'size': 72}
  • id: 153396934
    {'aut_label': '3T', 'centralizer': '72.g1', 'counter': 38, 'group_counter': 457, 'group_order': 17496, 'label': '3X', 'order': 3, 'powers': [38, 1], 'representative': 3912, 'size': 72}
  • id: 153396935
    {'aut_label': '3S', 'centralizer': '72.f1', 'counter': 39, 'group_counter': 457, 'group_order': 17496, 'label': '3Y', 'order': 3, 'powers': [39, 1], 'representative': 168, 'size': 72}
  • id: 153396937
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 40, 'group_counter': 457, 'group_order': 17496, 'label': '3Z1', 'order': 3, 'powers': [41, 1], 'representative': 1952, 'size': 72}
  • id: 153396938
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 41, 'group_counter': 457, 'group_order': 17496, 'label': '3Z-1', 'order': 3, 'powers': [40, 1], 'representative': 1960, 'size': 72}
  • id: 153396939
    {'aut_label': '3AA1', 'centralizer': '72.f1', 'counter': 42, 'group_counter': 457, 'group_order': 17496, 'label': '3AA1', 'order': 3, 'powers': [43, 1], 'representative': 224, 'size': 72}
  • id: 153396940
    {'aut_label': '3AA1', 'centralizer': '72.f1', 'counter': 43, 'group_counter': 457, 'group_order': 17496, 'label': '3AA-1', 'order': 3, 'powers': [42, 1], 'representative': 232, 'size': 72}
  • id: 153396941
    {'aut_label': '3AB1', 'centralizer': '72.g1', 'counter': 44, 'group_counter': 457, 'group_order': 17496, 'label': '3AB1', 'order': 3, 'powers': [45, 1], 'representative': 80, 'size': 72}
  • id: 153396942
    {'aut_label': '3AB1', 'centralizer': '72.g1', 'counter': 45, 'group_counter': 457, 'group_order': 17496, 'label': '3AB-1', 'order': 3, 'powers': [44, 1], 'representative': 88, 'size': 72}
  • id: 153396943
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 46, 'group_counter': 457, 'group_order': 17496, 'label': '3AC1', 'order': 3, 'powers': [47, 1], 'representative': 2168, 'size': 72}
  • id: 153396944
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 47, 'group_counter': 457, 'group_order': 17496, 'label': '3AC-1', 'order': 3, 'powers': [46, 1], 'representative': 3968, 'size': 72}
  • id: 153396945
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 48, 'group_counter': 457, 'group_order': 17496, 'label': '3AD1', 'order': 3, 'powers': [49, 1], 'representative': 1976, 'size': 72}
  • id: 153396946
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 49, 'group_counter': 457, 'group_order': 17496, 'label': '3AD-1', 'order': 3, 'powers': [48, 1], 'representative': 1984, 'size': 72}
  • id: 153396948
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 50, 'group_counter': 457, 'group_order': 17496, 'label': '3AE1', 'order': 3, 'powers': [51, 1], 'representative': 512, 'size': 72}
  • id: 153396949
    {'aut_label': '3Z1', 'centralizer': '72.e1', 'counter': 51, 'group_counter': 457, 'group_order': 17496, 'label': '3AE-1', 'order': 3, 'powers': [50, 1], 'representative': 520, 'size': 72}
  • id: 153396950
    {'aut_label': '3AB1', 'centralizer': '72.g1', 'counter': 52, 'group_counter': 457, 'group_order': 17496, 'label': '3AF1', 'order': 3, 'powers': [53, 1], 'representative': 3920, 'size': 72}
  • id: 153396951
    {'aut_label': '3AB1', 'centralizer': '72.g1', 'counter': 53, 'group_counter': 457, 'group_order': 17496, 'label': '3AF-1', 'order': 3, 'powers': [52, 1], 'representative': 3928, 'size': 72}
  • id: 153396952
    {'aut_label': '3AA1', 'centralizer': '72.f1', 'counter': 54, 'group_counter': 457, 'group_order': 17496, 'label': '3AG1', 'order': 3, 'powers': [55, 1], 'representative': 176, 'size': 72}
  • id: 153396953
    {'aut_label': '3AA1', 'centralizer': '72.f1', 'counter': 55, 'group_counter': 457, 'group_order': 17496, 'label': '3AG-1', 'order': 3, 'powers': [54, 1], 'representative': 184, 'size': 72}
  • id: 153396954
    {'aut_label': '4A', 'centralizer': '486.a1', 'counter': 56, 'group_counter': 457, 'group_order': 17496, 'label': '4A', 'order': 4, 'powers': [2, 56], 'representative': 9529, 'size': 486}
  • id: 153396955
    {'aut_label': '4B', 'centralizer': '486.e1', 'counter': 57, 'group_counter': 457, 'group_order': 17496, 'label': '4B', 'order': 4, 'powers': [2, 57], 'representative': 13926, 'size': 486}
  • id: 153396956
    {'aut_label': '4C', 'centralizer': '1458.c1', 'counter': 58, 'group_counter': 457, 'group_order': 17496, 'label': '4C', 'order': 4, 'powers': [2, 58], 'representative': 1975, 'size': 1458}
  • id: 153396957
    {'aut_label': '6A1', 'centralizer': '81.a1', 'counter': 59, 'group_counter': 457, 'group_order': 17496, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 4500, 'size': 81}
  • id: 153396959
    {'aut_label': '6A1', 'centralizer': '81.a1', 'counter': 60, 'group_counter': 457, 'group_order': 17496, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 16812, 'size': 81}
  • id: 153396960
    {'aut_label': '6B', 'centralizer': '162.a1', 'counter': 61, 'group_counter': 457, 'group_order': 17496, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 6276, 'size': 162}
  • id: 153396961
    {'aut_label': '6C', 'centralizer': '162.b1', 'counter': 62, 'group_counter': 457, 'group_order': 17496, 'label': '6C', 'order': 6, 'powers': [6, 2], 'representative': 1460, 'size': 162}
  • id: 153396962
    {'aut_label': '6D1', 'centralizer': '162.a1', 'counter': 63, 'group_counter': 457, 'group_order': 17496, 'label': '6D1', 'order': 6, 'powers': [7, 2], 'representative': 6324, 'size': 162}
  • id: 153396963
    {'aut_label': '6D1', 'centralizer': '162.a1', 'counter': 64, 'group_counter': 457, 'group_order': 17496, 'label': '6D-1', 'order': 6, 'powers': [8, 2], 'representative': 1788, 'size': 162}
  • id: 153396964
    {'aut_label': '6E1', 'centralizer': '162.b1', 'counter': 65, 'group_counter': 457, 'group_order': 17496, 'label': '6E1', 'order': 6, 'powers': [9, 2], 'representative': 11636, 'size': 162}
  • id: 153396965
    {'aut_label': '6E1', 'centralizer': '162.b1', 'counter': 66, 'group_counter': 457, 'group_order': 17496, 'label': '6E-1', 'order': 6, 'powers': [10, 2], 'representative': 11620, 'size': 162}
  • id: 153396966
    {'aut_label': '6F', 'centralizer': '324.a1', 'counter': 67, 'group_counter': 457, 'group_order': 17496, 'label': '6F', 'order': 6, 'powers': [11, 2], 'representative': 820, 'size': 324}
  • id: 153396967
    {'aut_label': '6G1', 'centralizer': '324.a1', 'counter': 68, 'group_counter': 457, 'group_order': 17496, 'label': '6G1', 'order': 6, 'powers': [12, 2], 'representative': 3716, 'size': 324}
  • id: 153396968
    {'aut_label': '6G1', 'centralizer': '324.a1', 'counter': 69, 'group_counter': 457, 'group_order': 17496, 'label': '6G-1', 'order': 6, 'powers': [13, 2], 'representative': 9532, 'size': 324}
  • id: 153396970
    {'aut_label': '12A1', 'centralizer': '486.a1', 'counter': 70, 'group_counter': 457, 'group_order': 17496, 'label': '12A1', 'order': 12, 'powers': [61, 56], 'representative': 5245, 'size': 486}
  • id: 153396971
    {'aut_label': '12A1', 'centralizer': '486.a1', 'counter': 71, 'group_counter': 457, 'group_order': 17496, 'label': '12A5', 'order': 12, 'powers': [61, 56], 'representative': 11077, 'size': 486}
  • id: 153396972
    {'aut_label': '12B1', 'centralizer': '486.e1', 'counter': 72, 'group_counter': 457, 'group_order': 17496, 'label': '12B1', 'order': 12, 'powers': [59, 57], 'representative': 2250, 'size': 486}
  • id: 153396973
    {'aut_label': '12B1', 'centralizer': '486.e1', 'counter': 73, 'group_counter': 457, 'group_order': 17496, 'label': '12B-1', 'order': 12, 'powers': [60, 57], 'representative': 8742, 'size': 486}
  • id: 153396974
    {'aut_label': '12C1', 'centralizer': '486.a1', 'counter': 74, 'group_counter': 457, 'group_order': 17496, 'label': '12C1', 'order': 12, 'powers': [60, 56], 'representative': 13001, 'size': 486}
  • id: 153396975
    {'aut_label': '12C1', 'centralizer': '486.a1', 'counter': 75, 'group_counter': 457, 'group_order': 17496, 'label': '12C-1', 'order': 12, 'powers': [59, 56], 'representative': 11021, 'size': 486}
  • id: 153396976
    {'aut_label': '12D1', 'centralizer': '486.e1', 'counter': 76, 'group_counter': 457, 'group_order': 17496, 'label': '12D1', 'order': 12, 'powers': [62, 57], 'representative': 14734, 'size': 486}
  • id: 153396977
    {'aut_label': '12D1', 'centralizer': '486.e1', 'counter': 77, 'group_counter': 457, 'group_order': 17496, 'label': '12D5', 'order': 12, 'powers': [62, 57], 'representative': 2414, 'size': 486}
  • id: 153396978
    {'aut_label': '12E1', 'centralizer': '486.a1', 'counter': 78, 'group_counter': 457, 'group_order': 17496, 'label': '12E1', 'order': 12, 'powers': [63, 56], 'representative': 13405, 'size': 486}
  • id: 153396979
    {'aut_label': '12E1', 'centralizer': '486.a1', 'counter': 79, 'group_counter': 457, 'group_order': 17496, 'label': '12E-1', 'order': 12, 'powers': [64, 56], 'representative': 6529, 'size': 486}
  • id: 153396981
    {'aut_label': '12E1', 'centralizer': '486.a1', 'counter': 80, 'group_counter': 457, 'group_order': 17496, 'label': '12E5', 'order': 12, 'powers': [64, 56], 'representative': 445, 'size': 486}
  • id: 153396982
    {'aut_label': '12E1', 'centralizer': '486.a1', 'counter': 81, 'group_counter': 457, 'group_order': 17496, 'label': '12E-5', 'order': 12, 'powers': [63, 56], 'representative': 49, 'size': 486}
  • id: 153396983
    {'aut_label': '12F1', 'centralizer': '486.e1', 'counter': 82, 'group_counter': 457, 'group_order': 17496, 'label': '12F1', 'order': 12, 'powers': [65, 57], 'representative': 14554, 'size': 486}
  • id: 153396984
    {'aut_label': '12F1', 'centralizer': '486.e1', 'counter': 83, 'group_counter': 457, 'group_order': 17496, 'label': '12F-1', 'order': 12, 'powers': [66, 57], 'representative': 13934, 'size': 486}
  • id: 153396985
    {'aut_label': '12F1', 'centralizer': '486.e1', 'counter': 84, 'group_counter': 457, 'group_order': 17496, 'label': '12F5', 'order': 12, 'powers': [66, 57], 'representative': 14546, 'size': 486}
  • id: 153396986
    {'aut_label': '12F1', 'centralizer': '486.e1', 'counter': 85, 'group_counter': 457, 'group_order': 17496, 'label': '12F-5', 'order': 12, 'powers': [65, 57], 'representative': 13942, 'size': 486}
  • id: 153396987
    {'aut_label': '12G1', 'centralizer': '1458.c1', 'counter': 86, 'group_counter': 457, 'group_order': 17496, 'label': '12G1', 'order': 12, 'powers': [59, 58], 'representative': 12955, 'size': 1458}
  • id: 153396988
    {'aut_label': '12G1', 'centralizer': '1458.c1', 'counter': 87, 'group_counter': 457, 'group_order': 17496, 'label': '12G-1', 'order': 12, 'powers': [60, 58], 'representative': 14287, 'size': 1458}
• 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: 14829551
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 14829562
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14829573
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14829584
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14829595
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 2, 0, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 14829599
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -2, 0, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 14829600
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14829601
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.2d', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, -2, 4, 4, -2, -2, -2, -2, -2, 4, 4, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -4, -4, -4, 2, -4, -4, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14829554
    {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8a', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829555
    {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8b', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829556
    {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8c', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829557
    {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8d', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829558
    {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8e', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -4, 2, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, 2, 2, 2, 2, -1, 2, -4, -1, -1, -1, 2, 5, -1, -1, 2, 2, -4, -4, -1, -1, -1, -1, -1, -1, 2, 2, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829559
    {'cdim': 8, 'counter': 17, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8f', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -4, 2, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, 2, 2, 2, 2, -1, 2, 5, -1, -1, -1, 2, -4, -1, -1, 2, 2, 5, 5, -1, -1, -1, -1, -1, -1, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829560
    {'cdim': 8, 'counter': 18, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8g', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, -4, 2, 2, 2, 2, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, -1, -4, 2, -1, -1, -1, 5, 2, -1, -1, -4, -4, 2, 2, -1, -1, -1, -1, -1, -1, 5, 5, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829561
    {'cdim': 8, 'counter': 19, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8h', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, -4, 2, 2, 2, 2, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, -1, 5, 2, -1, -1, -1, -4, 2, -1, -1, 5, 5, 2, 2, -1, -1, -1, -1, -1, -1, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829563
    {'cdim': 8, 'counter': 20, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8i', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 5, 2, 2, 2, 2, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 5, -1, -4, 2, -1, -1, -1, -4, 2, -1, -1, -4, -4, 2, 2, -1, -1, -1, -1, -1, -1, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829564
    {'cdim': 8, 'counter': 21, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8j', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 2, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 5, 2, 2, 2, 2, -1, 2, -4, -1, -1, -1, 2, -4, -1, -1, 2, 2, -4, -4, -1, -1, -1, -1, -1, -1, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829602
    {'cdim': 6, 'counter': 9, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.6a', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, -6, 12, 3, 3, -6, -6, -6, 3, 3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, -4, -1, -1, 2, 2, 2, -1, -1, -2, -2, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829552
    {'cdim': 6, 'counter': 10, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.6b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, -6, 12, 3, 3, -6, -6, -6, 3, 3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 2, 2, -4, -1, -1, 2, 2, 2, -1, -1, 2, 2, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829565
    {'cdim': 8, 'counter': 22, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8k', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 16, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -8, -8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829566
    {'cdim': 8, 'counter': 23, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8l', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 16, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -8, -8, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829567
    {'cdim': 8, 'counter': 24, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8m', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 16, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -8, -8, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829568
    {'cdim': 8, 'counter': 25, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8n', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, -2, -2, -2, -2, -2, -2, -2, -8, -8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829569
    {'cdim': 8, 'counter': 26, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8o', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -8, 4, -8, -8, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, 4, -8, -2, -2, -2, 4, 10, 1, 1, -2, -2, 4, 4, 1, 1, 1, 1, 1, 1, -2, -2, -5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829570
    {'cdim': 8, 'counter': 27, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8p', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -8, 4, -8, -8, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, 4, 10, -2, -2, -2, 4, -8, 1, 1, -2, -2, -5, -5, 1, 1, 1, 1, 1, 1, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829571
    {'cdim': 8, 'counter': 28, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8q', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, 4, -8, 4, 4, -2, -2, -8, -8, 4, 4, -2, -2, -2, -2, 4, 4, 4, 4, -2, -8, 4, -2, -2, -2, 10, 4, 1, 1, 4, 4, -2, -2, 1, 1, 1, 1, 1, 1, -5, -5, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829572
    {'cdim': 8, 'counter': 29, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8r', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, 4, -8, 4, 4, -2, -2, -8, -8, 4, 4, -2, -2, -2, -2, 4, 4, 4, 4, -2, 10, 4, -2, -2, -2, -8, 4, 1, 1, -5, -5, -2, -2, 1, 1, 1, 1, 1, 1, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829574
    {'cdim': 8, 'counter': 30, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8s', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, 4, 10, 4, 4, -2, -2, 10, 10, -5, -5, -2, -2, -2, -2, -5, -5, -5, -5, -2, -8, 4, -2, -2, -2, -8, 4, 1, 1, 4, 4, -2, -2, 1, 1, 1, 1, 1, 1, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829575
    {'cdim': 8, 'counter': 31, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.8t', 'multiplicity': 2, 'nt': [24, 4975], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, 10, 4, 10, 10, -5, -5, 4, 4, -2, -2, -5, -5, -5, -5, -2, -2, -2, -2, -2, 4, -8, -2, -2, -2, 4, -8, 1, 1, -2, -2, 4, 4, 1, 1, 1, 1, 1, 1, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829576
    {'cdim': 9, 'counter': 32, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.9a', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, -9, -9, 18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14829577
    {'cdim': 9, 'counter': 33, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.9b', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, -9, -9, 18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -2, -2, -1, -1, 1, 1, 2, 2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14829578
    {'cdim': 9, 'counter': 34, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.9c', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, -9, -9, 18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, 1, 1, -1, -1, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 14829579
    {'cdim': 9, 'counter': 35, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.9d', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, -9, -9, 18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14829582
    {'cdim': 18, 'counter': 38, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18a', 'multiplicity': 1, 'nt': [27, 420], 'qdim': 18, 'qvalues': [18, 2, 18, 18, -9, 18, -9, -9, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829583
    {'cdim': 18, 'counter': 39, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, 18, 18, -9, 18, -9, -9, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 1, 1, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829553
    {'cdim': 6, 'counter': 11, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.6c', 'multiplicity': 4, 'nt': [36, 6806], 'qdim': 24, 'qvalues': [24, 8, -12, -12, -12, 24, 6, 6, -12, -12, -12, 6, 6, 12, 12, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, 12, 12, 12, 12, -6, -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, -4, -4, -4, 8, 2, 2, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829580
    {'cdim': 12, 'counter': 36, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.12a', 'multiplicity': 2, 'nt': [36, 10908], 'qdim': 24, 'qvalues': [24, 8, -12, -12, -12, -12, 6, 6, 6, 6, 6, -3, -3, 12, 12, -6, -6, 3, 3, -6, -6, 3, 3, 3, 3, -6, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829581
    {'cdim': 12, 'counter': 37, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.12b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -12, -12, -12, -12, 6, 6, 6, 6, 6, -3, -3, 12, 12, -6, -6, 3, 3, -6, -6, 3, 3, 3, 3, -6, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829585
    {'cdim': 18, 'counter': 40, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18c', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 4, -18, -18, 36, -18, -18, -18, 9, 9, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, 1, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 14829586
    {'cdim': 18, 'counter': 41, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18d', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, 4, -18, -18, 36, -18, -18, -18, 9, 9, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 14829587
    {'cdim': 18, 'counter': 42, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18e', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, -18, -18, 36, 36, -18, -18, -18, -18, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829588
    {'cdim': 18, 'counter': 43, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18f', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, 36, 36, -18, 36, -18, -18, 36, 36, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14829597
    {'cdim': 36, 'counter': 51, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.36a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 4, 36, 36, -18, -18, -18, -18, -18, -18, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829598
    {'cdim': 36, 'counter': 52, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.36b', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, 36, 36, -18, -18, -18, -18, -18, -18, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14829590
    {'cdim': 24, 'counter': 45, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, -24, 12, 12, 12, 12, 12, -6, -6, -12, 6, 6, 6, -3, -3, -3, -3, -12, -12, -3, -3, 6, 6, -3, -3, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829591
    {'cdim': 24, 'counter': 46, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, -24, 12, 12, 12, 12, 12, -6, -6, -12, 6, 6, 6, -3, -3, -3, -3, 15, 15, -3, -3, 6, 6, -3, -3, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829592
    {'cdim': 24, 'counter': 47, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, -24, 12, 12, 12, 12, 12, -6, -6, 6, -12, -3, -3, -12, -12, 6, 6, -3, -3, 15, 15, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829593
    {'cdim': 24, 'counter': 48, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24d', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, -24, 12, 12, 12, 12, 12, -6, -6, 6, -12, -3, -3, 15, 15, 6, 6, -3, -3, -12, -12, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829594
    {'cdim': 24, 'counter': 49, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24e', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 48, 12, 12, -24, -24, -24, 12, 12, -12, 6, 6, 6, 6, 6, -3, -3, -3, -3, 6, 6, -12, -12, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829596
    {'cdim': 24, 'counter': 50, 'faithful': True, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.24f', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 48, 12, 12, -24, -24, -24, 12, 12, 6, -12, -3, -3, -3, -3, 6, 6, 6, 6, -3, -3, 6, 6, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14829589
    {'cdim': 18, 'counter': 44, 'faithful': False, 'group': '17496.ro', 'group_order': 17496, 'image': None, 'label': '17496.ro.18g', 'multiplicity': 4, 'nt': [216, 0], 'qdim': 72, 'qvalues': [72, -8, -36, -36, 72, -36, -36, -36, 18, 18, -36, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -8, 4, 4, 4, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 34481082
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 17496, 'label': '17496.ro.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34481093
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 8748, 'label': '17496.ro.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34481104
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 8748, 'label': '17496.ro.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34481115
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 8748, 'label': '17496.ro.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34481126
    {'center': '6.a1', 'center_index': 6, 'center_order': 2916, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ro.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481137
    {'center': '6.a1', 'center_index': 6, 'center_order': 2916, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 1458, 'label': '17496.ro.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481148
    {'center': '4.a1', 'center_index': 4, 'center_order': 4374, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.a1', 'kernel_order': 2187, 'label': '17496.ro.2c', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481159
    {'center': '12.a1', 'center_index': 12, 'center_order': 1458, 'counter': 8, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1', 'kernel_order': 729, 'label': '17496.ro.2d1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34481168
    {'center': '12.a1', 'center_index': 12, 'center_order': 1458, 'counter': 9, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1', 'kernel_order': 729, 'label': '17496.ro.2d2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34481083
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 10, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6a1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481084
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 11, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6a2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481085
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 12, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6b1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481086
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 13, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6b2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481087
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 14, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6c1', 'nt': [36, 6806], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481088
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 15, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6c2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481089
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 16, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6c3', 'nt': [36, 6806], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481090
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 17, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.6c4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481091
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 18, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.ro.8a', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481092
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.ro.8b', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481094
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 20, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.ro.8c', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481095
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 21, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.ro.8d', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481096
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8e', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481097
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 23, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8f', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481098
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 24, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8g', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481099
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 25, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8h', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481100
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 26, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8i', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481101
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 27, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.ro.8j', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[5, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481102
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 28, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8k1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481103
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 29, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8k2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481105
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 30, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8l1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481106
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 31, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8l2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481107
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 32, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8m1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481108
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 33, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8m2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481109
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 34, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8n1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481110
    {'center': '216.a1', 'center_index': 216, 'center_order': 81, 'counter': 35, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ro.8n2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481111
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 36, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8o1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481112
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 37, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8o2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481113
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 38, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8p1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481114
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 39, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8p2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481116
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 40, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8q1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481117
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8q2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481118
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 42, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8r1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481119
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8r2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481120
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8s1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481121
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8s2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481122
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8t1', 'nt': [24, 4975], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481123
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3931', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ro.8t2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[2, 0]], [[5, 0]], [[5, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481124
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 48, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9a1', 'nt': [54, 0], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, 0]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 1]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 34481125
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 49, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9a2', 'nt': [54, 2], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 0]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, -1]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 34481127
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 50, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9b1', 'nt': [54, 0], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, 0]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 1]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 34481128
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 51, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9b2', 'nt': [54, 2], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 0]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, -1]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 34481129
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 52, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9c1', 'nt': [54, 0], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, 0]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 1]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 34481130
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 53, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9c2', 'nt': [54, 2], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 0]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, -1]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 34481131
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 54, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9d1', 'nt': [54, 0], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, 0]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 1]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 34481132
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 55, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.9d2', 'nt': [54, 2], 'q_character': None, 'values': [[[9, 0]], [[1, 0]], [[9, 1]], [[9, -1]], [[9, 0]], [[9, 0]], [[9, -1]], [[9, 1]], [[9, -1]], [[9, 1]], [[9, 0]], [[9, -1]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 34481133
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 56, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.12a1', 'nt': [36, 10908], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, -1]], [[12, 1]], [[-6, 0]], [[-6, 0]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481134
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 57, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.12a2', 'nt': [36, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, 1]], [[12, -1]], [[-6, 0]], [[-6, 0]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481135
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 58, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.12b1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, -1]], [[12, 1]], [[-6, 0]], [[-6, 0]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481136
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 59, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.12b2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 1]], [[12, -1]], [[-6, 0]], [[-6, 0]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481138
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 60, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.b1', 'kernel_order': 9, 'label': '17496.ro.18a', 'nt': [27, 420], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481139
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 61, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.b1', 'kernel_order': 9, 'label': '17496.ro.18b', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481140
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 62, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18c1', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, -1]], [[18, 1]], [[18, 0]], [[-9, 0]], [[18, 1]], [[18, -1]], [[-9, 1]], [[-9, -1]], [[-9, 0]], [[-9, 1]], [[-9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 34481141
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 63, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18c2', 'nt': [54, 2], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 1]], [[18, -1]], [[18, 0]], [[-9, 0]], [[18, -1]], [[18, 1]], [[-9, -1]], [[-9, 1]], [[-9, 0]], [[-9, -1]], [[-9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34481142
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 64, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18d1', 'nt': [108, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, -1]], [[18, 1]], [[18, 0]], [[-9, 0]], [[18, 1]], [[18, -1]], [[-9, 1]], [[-9, -1]], [[-9, 0]], [[-9, 1]], [[-9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 34481143
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 65, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18d2', 'nt': [108, 2], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 1]], [[18, -1]], [[18, 0]], [[-9, 0]], [[18, -1]], [[18, 1]], [[-9, -1]], [[-9, 1]], [[-9, 0]], [[-9, -1]], [[-9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34481144
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 66, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.18e1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, -1]], [[18, 1]], [[18, 0]], [[18, 0]], [[18, 1]], [[18, -1]], [[18, 1]], [[18, -1]], [[18, 0]], [[18, 1]], [[18, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481145
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 67, 'cyclotomic_n': 3, 'dim': 18, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3561', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.c1', 'kernel_order': 9, 'label': '17496.ro.18e2', 'nt': [216, 2], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 1]], [[18, -1]], [[18, 0]], [[18, 0]], [[18, -1]], [[18, 1]], [[18, -1]], [[18, 1]], [[18, 0]], [[18, -1]], [[18, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481146
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 68, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.b1', 'kernel_order': 9, 'label': '17496.ro.18f1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481147
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 69, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.b1', 'kernel_order': 9, 'label': '17496.ro.18f2', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481149
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 70, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18g1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[-18, 2]], [[18, 4]], [[18, 0]], [[-9, 0]], [[18, 4]], [[-18, 2]], [[-9, 4]], [[9, 2]], [[-9, 0]], [[-9, 4]], [[9, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[1, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 34481150
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 71, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18g2', 'nt': [216, 4], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 4]], [[-18, 2]], [[18, 0]], [[-9, 0]], [[-18, 2]], [[18, 4]], [[9, 2]], [[-9, 4]], [[-9, 0]], [[9, 2]], [[-9, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 34481151
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 72, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18g3', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[-18, 2]], [[18, 4]], [[18, 0]], [[-9, 0]], [[18, 4]], [[-18, 2]], [[-9, 4]], [[9, 2]], [[-9, 0]], [[-9, 4]], [[9, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[1, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 34481152
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 73, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 0, 'kernel': '5832.b1', 'kernel_order': 3, 'label': '17496.ro.18g4', 'nt': [216, 4], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 4]], [[-18, 2]], [[18, 0]], [[-9, 0]], [[-18, 2]], [[18, 4]], [[9, 2]], [[-9, 4]], [[-9, 0]], [[9, 2]], [[-9, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 34481153
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 74, 'cyclotomic_n': 3, 'dim': 24, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.24a1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[-6, 0]], [[3, 0]], [[-6, -1]], [[-6, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[-3, 0], [6, 1]], [[-9, 0], [-6, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[9, 0], [3, 1]], [[6, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481154
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 75, 'cyclotomic_n': 3, 'dim': 24, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.24a2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[-6, 0]], [[3, 0]], [[-6, 1]], [[-6, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[-9, 0], [-6, 1]], [[-3, 0], [6, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[6, 0], [-3, 1]], [[9, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481155
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 76, 'cyclotomic_n': 3, 'dim': 24, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.24b1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[-6, 0]], [[3, 0]], [[-6, -1]], [[-6, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[6, 0], [-3, 1]], [[9, 0], [3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[-9, 0], [-6, 1]], [[-3, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481156
    {'center': '1944.b1', 'center_index': 1944, 'center_order': 9, 'counter': 77, 'cyclotomic_n': 3, 'dim': 24, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '5832.nw', 'image_order': 5832, 'indicator': 0, 'kernel': '5832.c1', 'kernel_order': 3, 'label': '17496.ro.24b2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[-6, 0]], [[3, 0]], [[-6, 1]], [[-6, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[9, 0], [3, 1]], [[6, 0], [-3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[-3, 0], [6, 1]], [[-9, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481157
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 78, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24c1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[3, 0]], [[-6, 0]], [[3, -1]], [[3, 1]], [[-3, 0], [6, 1]], [[-9, 0], [-6, 1]], [[-6, 1]], [[-6, -1]], [[3, -1]], [[3, 1]], [[9, 0], [3, 1]], [[6, 0], [-3, 1]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481158
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 79, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24c2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[3, 0]], [[-6, 0]], [[3, 1]], [[3, -1]], [[-9, 0], [-6, 1]], [[-3, 0], [6, 1]], [[-6, -1]], [[-6, 1]], [[3, 1]], [[3, -1]], [[6, 0], [-3, 1]], [[9, 0], [3, 1]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481160
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 80, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24d1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[3, 0]], [[-6, 0]], [[3, -1]], [[3, 1]], [[6, 0], [-3, 1]], [[9, 0], [3, 1]], [[-6, 1]], [[-6, -1]], [[3, -1]], [[3, 1]], [[-9, 0], [-6, 1]], [[-3, 0], [6, 1]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481161
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 81, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24d2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[-12, -1]], [[-12, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[3, 0]], [[-6, 0]], [[3, 1]], [[3, -1]], [[9, 0], [3, 1]], [[6, 0], [-3, 1]], [[-6, -1]], [[-6, 1]], [[3, 1]], [[3, -1]], [[-3, 0], [6, 1]], [[-9, 0], [-6, 1]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481162
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 82, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24e1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[24, 0]], [[-12, 1]], [[-12, -1]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[-6, 0]], [[3, 0]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[-6, 1]], [[-6, -1]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481163
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 83, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24e2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[24, 0]], [[-12, -1]], [[-12, 1]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[-6, 0]], [[3, 0]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[-6, -1]], [[-6, 1]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34481164
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 84, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24f1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[-12, 0]], [[24, 0]], [[-12, 1]], [[-12, -1]], [[24, 1]], [[24, -1]], [[-12, 0]], [[-12, 1]], [[-12, -1]], [[3, 0]], [[-6, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-6, 1]], [[-6, -1]], [[-6, -1]], [[-6, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481165
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 85, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ro', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ro.24f2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[-12, 0]], [[24, 0]], [[-12, -1]], [[-12, 1]], [[24, -1]], [[24, 1]], [[-12, 0]], [[-12, -1]], [[-12, 1]], [[3, 0]], [[-6, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-6, -1]], [[-6, 1]], [[-6, 1]], [[-6, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481166
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 86, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.ro.36a', 'nt': [54, 0], 'q_character': None, 'values': [[[36, 0]], [[4, 0]], [[36, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34481167
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 87, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.ro', 'group_counter': 457, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': -1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.ro.36b', 'nt': [216, 0], 'q_character': None, 'values': [[[36, 0]], [[-4, 0]], [[36, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 157833240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 17496, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '17496.ro.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ro', 'subgroup_hash': 6736393944771584879, 'subgroup_order': 17496, 'subgroup_tex': '\\He_3^2:C_4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 157833351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 8748, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8526571669698341106, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^3.C_3^4.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 8748, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4729191320505677415, 'subgroup_order': 8748, 'subgroup_tex': 'C_3\\times C_3^4.C_3^2.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 8748, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8960208856555699946, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^5.C_3^2.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2916, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.nw', 'subgroup_hash': 6838393720671276366, 'subgroup_order': 5832, 'subgroup_tex': '\\He_3^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 157833795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 4374, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2', 'D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6530252586840099560, 'subgroup_order': 4374, 'subgroup_tex': 'C_3\\times (C_3^3.C_3^3):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 2916, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ek', 'subgroup_hash': 1845857091967694541, 'subgroup_order': 2916, 'subgroup_tex': '\\He_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1458, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3960894827536741230, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^2.C_3^4.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1458, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ek', 'subgroup_hash': 1845857091967694541, 'subgroup_order': 2916, 'subgroup_tex': '\\He_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 2187, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '17496.ro.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L2', 'C3', 'F', 'L2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9107', 'subgroup_hash': 3663461610157526950, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^4.C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 157833252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3557', 'subgroup_hash': 3557, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157833263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 1458, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1576', 'subgroup_hash': 1576, 'subgroup_order': 1458, 'subgroup_tex': '\\He_3^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1761', 'subgroup_hash': 1761, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '972.880', 'subgroup_hash': 880, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.879', 'subgroup_hash': 879, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 729, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '729.453', 'subgroup_hash': 453, 'subgroup_order': 729, 'subgroup_tex': '\\He_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.498', 'subgroup_hash': 498, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.453', 'subgroup_hash': 453, 'subgroup_order': 729, 'subgroup_tex': '\\He_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.453', 'subgroup_hash': 453, 'subgroup_order': 729, 'subgroup_tex': '\\He_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.453', 'subgroup_hash': 453, 'subgroup_order': 729, 'subgroup_tex': '\\He_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.453', 'subgroup_hash': 453, 'subgroup_order': 729, 'subgroup_tex': '\\He_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.553', 'subgroup_hash': 553, 'subgroup_order': 648, 'subgroup_tex': 'C_3:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157833529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.553', 'subgroup_hash': 553, 'subgroup_order': 648, 'subgroup_tex': 'C_3:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157833540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.243', 'subgroup_hash': 243, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.243', 'subgroup_hash': 243, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.243', 'subgroup_hash': 243, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.54.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157834011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['C4', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • id: 157834016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • id: 157834017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • id: 157834018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157834029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.br2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bw3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.by2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.by2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.by3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.by3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.88', 'subgroup_hash': 88, 'subgroup_order': 216, 'subgroup_tex': '\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157833287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.o2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157833354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.108.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157833375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.162.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 221, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 27, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157833488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ea2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ea2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ea3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ea3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ec2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ec2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ed2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ed2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ed3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ed3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eq3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eq3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.et2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.et2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.et3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.et3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.eu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.216.ev2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ev2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.243.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.243.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.324.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157833604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 157833615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157833617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.486.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157833620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': True, 'core_order': 27, 'counter': 441, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.730', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 730, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C5', 'S', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833633
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833727
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ej2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ej2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833782
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833799
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833803
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.648.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157833810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.729.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '729.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.729.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '729.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.729.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '729.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157833813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': 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: 157833831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 157833854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.972.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 655, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 656, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 657, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833860
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 658, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833861
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833863
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833864
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 662, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833866
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833869
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1458.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': 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: 157833870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': True, 'core_order': 9, 'counter': 667, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.3931', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3931, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^5:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'D3', 'C6', 'Phi', 'D3', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': True, 'core_order': 9, 'counter': 668, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.3559', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3559, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': True, 'core_order': 9, 'counter': 669, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.ro.1944.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.3561', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3561, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3.\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157833874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 3, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 3, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 3, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833894
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833920
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.de2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.de2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.df2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.df2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.1944.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': 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: 157833970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '17496.ro.2187.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2187.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2187, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 2}
  • id: 157833971
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 758, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 759, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 760, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833975
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833979
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833980
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833981
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833982
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ro.2916.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': 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: 157833983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 769, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.4374.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4374.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4374, 'quotient_simple': 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: 157833985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.4374.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4374.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4374, 'quotient_simple': 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: 157833986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 771, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.4374.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4374.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4374, 'quotient_simple': 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: 157833987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': True, 'central_factor': False, 'centralizer_order': 17496, 'characteristic': True, 'core_order': 3, 'counter': 772, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '17496.ro.5832.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5832.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 745905227323407307, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5832, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3.C_3^5.Q_8', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0', 'Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': True, 'core_order': 3, 'counter': 773, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '17496.ro.5832.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5832.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5166056731452399813, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5832, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3.C_3^5.Q_8', 'simple': True, 'solvable': True, 'special_labels': ['C7', 'C7'], '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: 157833989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': True, 'core_order': 3, 'counter': 774, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '17496.ro.5832.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5832.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '5832.nw', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6838393720671276366, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5832, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3^2:Q_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157833990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': False, 'core_order': 1, 'counter': 776, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 782, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157833999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 783, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 784, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834001
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834003
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.5832.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157834005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 789, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.ro.8748.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8748.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8748, '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: 157834007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.ro', 'ambient_counter': 457, 'ambient_order': 17496, 'ambient_tex': '\\He_3^2:C_4.S_3', 'central': True, 'central_factor': False, 'centralizer_order': 17496, 'characteristic': True, 'core_order': 1, 'counter': 790, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '17496.ro.17496.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '17496.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '17496.ro', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6736393944771584879, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 17496, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3^2:C_4.S_3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C8', 'PC', 'U1', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 157833450
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '108.bl1'], 'contains': ['648.bl1', '648.cd1', '648.cg1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [3925, -1, 8771, -1], 'generators': [12320, 2448, 3240], 'label': '17496.ro.216.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '216.cp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833689
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bs1', '216.co1', '216.cv1'], 'contains': ['1944.r1', '1944.s1', '1944.u1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [2635, -1, 4733, -1], 'generators': [3920, 7200], 'label': '17496.ro.648.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.k1', 'old_label': '648.ck1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ck1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833690
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bt1', '216.cq1', '216.cx1'], 'contains': ['1944.r1', '1944.t1', '1944.u1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1274, -1, 4418, -1], 'generators': [5024, 2880], 'label': '17496.ro.648.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.m1', 'old_label': '648.cl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cl1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833784
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '18.b1'], 'contains': ['108.j1', '162.e1', '162.l1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [776, -1, 8897, -1], 'generators': [6, 5832, 4752, 648, 12, 8016], 'label': '17496.ro.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '54.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833845
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['324.k1', '324.o1', '324.bc1', '324.cg1'], 'contains': ['1944.bv1', '2916.f1', '2916.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [2821, -1, 8081, -1], 'generators': [9300, 6488, 5928], 'label': '17496.ro.972.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.bd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833846
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.l1', '324.p1', '324.bd1', '324.ch1'], 'contains': ['1944.bw1', '2916.f1', '2916.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [937, -1, 7755, -1], 'generators': [9300, 6488, 6720], 'label': '17496.ro.972.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.be1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833240
    {'ambient': '17496.ro', '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': '5832.a1', 'complements': ['17496.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [938, 3898, 8918, 2396], 'generators': [3469, 12312, 9240, 4824, 5832, 6, 12320, 14256, 12528, 9300], 'label': '17496.ro.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 157833241
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': ['2187.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.a1', '24.b1', '24.c1', '24.d1', '24.e1', '24.f1', '24.g1', '24.h1', '24.i1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3616, 3520, 4219, 2376], 'generators': [12320, 14904, 15360, 7200, 10584], 'label': '17496.ro.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['24.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': None, 'quotient_action_image': '8.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157833242
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.h1', '24.i1'], 'contains': ['216.g1', '216.k1', '216.m1', '216.v1', '216.x1', '216.bd1', '216.be1', '216.bn1', '216.bo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3751, -1, 4123, -1], 'generators': [9512, 888, 2448], 'label': '17496.ro.72.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833243
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.d1', '24.g1', '24.h1', '24.i1'], 'contains': ['216.f1', '216.k1', '216.m1', '216.o1', '216.t1', '216.u1', '216.w1', '216.bd1', '216.bf1', '216.bg1', '216.bg2', '216.bl1', '216.bm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3911, -1, 4251, -1], 'generators': [4976, 888, 2448], 'label': '17496.ro.72.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833244
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.h1', '24.i1'], 'contains': ['216.h1', '216.l1', '216.m1', '216.v1', '216.z1', '216.bd1', '216.bf1', '216.bt1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3941, -1, 3900, -1], 'generators': [7280, 2472, 15120], 'label': '17496.ro.72.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833245
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.d1', '24.f1', '24.h1', '24.i1'], 'contains': ['216.f1', '216.l1', '216.m1', '216.n1', '216.t1', '216.u1', '216.y1', '216.bd1', '216.be1', '216.bg1', '216.bg2', '216.br1', '216.bs1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4000, -1, 4155, -1], 'generators': [8000, 11040, 7416], 'label': '17496.ro.72.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833246
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.e1', '24.f1', '24.g1', '24.h1'], 'contains': ['216.f1', '216.i1', '216.j1', '216.m1', '216.t1', '216.u1', '216.w1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.bb1', '216.bc1', '216.ee1', '216.eh1', '216.et1', '216.et2', '216.et3'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5861, -1, 3464, -1], 'generators': [7280, 9024, 10584, 5832], 'label': '17496.ro.72.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833247
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.g1', '24.h1'], 'contains': ['216.h1', '216.i1', '216.k1', '216.n1', '216.u1', '216.v1', '216.w1', '216.ba1', '216.bb1', '216.ef1', '216.ei1', '216.eu1', '216.eu2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5812, -1, 3388, -1], 'generators': [9512, 15360, 2448, 5832], 'label': '17496.ro.72.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833248
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.f1', '24.h1'], 'contains': ['216.g1', '216.i1', '216.l1', '216.o1', '216.t1', '216.v1', '216.y1', '216.ba1', '216.bc1', '216.eg1', '216.ej1', '216.ev1', '216.ev2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5612, -1, 3168, -1], 'generators': [9512, 11256, 7200, 5832], 'label': '17496.ro.72.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833249
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.h1', '24.i1'], 'contains': ['216.f1', '216.g1', '216.h1', '216.i1', '216.m1', '216.p1', '216.t1', '216.u1', '216.v1', '216.ea1', '216.ea2', '216.ea3', '216.ek1', '216.en1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6339, -1, 3229, -1], 'generators': [7280, 2472, 10584, 5832], 'label': '17496.ro.72.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833250
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.g1', '24.i1'], 'contains': ['216.f1', '216.h1', '216.i1', '216.o1', '216.q1', '216.w1', '216.x1', '216.eb1', '216.eb2', '216.el1', '216.eo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6446, -1, 3108, -1], 'generators': [5192, 456, 216, 5832], 'label': '17496.ro.72.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833251
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.f1', '24.i1'], 'contains': ['216.f1', '216.g1', '216.i1', '216.n1', '216.r1', '216.y1', '216.z1', '216.ec1', '216.ec2', '216.em1', '216.ep1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6380, -1, 3048, -1], 'generators': [9512, 15360, 7200, 5832], 'label': '17496.ro.72.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833252
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['18.d1', '18.e1', '18.f1', '27.a1', '27.b1', '81.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [950, -1, 9598, -1], 'generators': [3469, 744, 13608, 7206, 12320, 12312, 5832, 9300], 'label': '17496.ro.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
  • id: 157833253
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.h1', '24.i1'], 'contains': ['216.m1', '216.n1', '216.o1', '216.p1', '216.bd1', '216.be1', '216.bf1', '216.bg1', '216.bg2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3876, -1, 4655, -1], 'generators': [4976, 15360, 15624], 'label': '17496.ro.72.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833254
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.b1', '24.f1', '36.o1'], 'contains': ['216.j1', '216.l1', '216.r1', '216.bh1', '216.bj1', '216.bp1', '216.bv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2571, -1, 4442, -1], 'generators': [15360, 7200, 15120], 'label': '17496.ro.72.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833255
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.c1', '24.g1', '36.p1'], 'contains': ['216.j1', '216.k1', '216.q1', '216.bh1', '216.bi1', '216.bp1', '216.bq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2297, -1, 4936, -1], 'generators': [10824, 7200, 10584], 'label': '17496.ro.72.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833256
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.d1', '24.h1', '36.q1'], 'contains': ['216.a1', '216.j1', '216.k1', '216.l1', '216.p1', '216.bh1', '216.bi1', '216.bj1', '216.bk1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3381, -1, 4968, -1], 'generators': [15360, 2448, 14904], 'label': '17496.ro.72.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833257
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.g1', '24.i1'], 'contains': ['216.m1', '216.n1', '216.q1', '216.bl1', '216.bm1', '216.bn1', '216.bo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2096, -1, 4219, -1], 'generators': [7280, 4488, 10584], 'label': '17496.ro.72.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833258
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.f1', '24.i1'], 'contains': ['216.m1', '216.o1', '216.r1', '216.br1', '216.bs1', '216.bt1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2182, -1, 3868, -1], 'generators': [8000, 15360, 7200], 'label': '17496.ro.72.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833259
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.i1'], 'contains': ['216.f1', '216.g1', '216.h1', '216.m1', '216.n1', '216.o1', '216.s1', '216.ed1', '216.ed2', '216.ed3', '216.er1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6104, -1, 2987, -1], 'generators': [5192, 15360, 10584, 5832], 'label': '17496.ro.72.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833260
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.e1', '24.i1', '36.r1'], 'contains': ['216.j1', '216.k1', '216.l1', '216.p1', '216.q1', '216.r1', '216.s1', '216.eq1', '216.eq2', '216.eq3', '216.es1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5019, -1, 3584, -1], 'generators': [15360, 10584, 14904, 5832], 'label': '17496.ro.72.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833261
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.g1', '24.h1'], 'contains': ['216.u1', '216.v1', '216.w1', '216.bc1', '216.bf1', '216.bh1', '216.bn1', '216.br1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3077, -1, 4187, -1], 'generators': [4976, 888, 17352], 'label': '17496.ro.72.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833262
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.f1', '24.h1'], 'contains': ['216.t1', '216.v1', '216.y1', '216.bb1', '216.be1', '216.bh1', '216.bm1', '216.bo1', '216.bt1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2117, -1, 4314, -1], 'generators': [9512, 10824, 2448], 'label': '17496.ro.72.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833263
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.b1', '6.c1'], 'contains': ['24.a1', '36.o1', '36.p1', '36.q1', '36.r1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2265, 5559, 7208, 4318], 'generators': [9300, 648, 3240, 14712, 5832, 7200, 9936], 'label': '17496.ro.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157833264
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.d1', '24.f1', '24.g1', '24.h1'], 'contains': ['216.t1', '216.u1', '216.w1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.bd1', '216.bg1', '216.bg2', '216.bh1', '216.bl1', '216.bs1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4546, -1, 4378, -1], 'generators': [4976, 11040, 15624], 'label': '17496.ro.72.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833265
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.g1', '24.h1'], 'contains': ['216.t1', '216.v1', '216.w1', '216.bb1', '216.bd1', '216.bi1', '216.bl1', '216.bn1', '216.bo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2318, -1, 4410, -1], 'generators': [9512, 13632, 2448], 'label': '17496.ro.72.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833266
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.g1', '24.h1'], 'contains': ['216.u1', '216.w1', '216.x1', '216.ba1', '216.bf1', '216.bg1', '216.bg2', '216.bi1', '216.bm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3801, -1, 4840, -1], 'generators': [14768, 11832, 14904], 'label': '17496.ro.72.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833267
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.f1', '24.h1'], 'contains': ['216.u1', '216.v1', '216.y1', '216.bc1', '216.bd1', '216.bj1', '216.bs1', '216.bt1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2668, -1, 4028, -1], 'generators': [8000, 11040, 7200], 'label': '17496.ro.72.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833268
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.f1', '24.h1'], 'contains': ['216.t1', '216.y1', '216.z1', '216.ba1', '216.be1', '216.bg1', '216.bg2', '216.bj1', '216.br1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3962, -1, 4808, -1], 'generators': [8000, 11040, 2448], 'label': '17496.ro.72.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833269
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.h1'], 'contains': ['216.t1', '216.u1', '216.v1', '216.ba1', '216.bd1', '216.be1', '216.bf1', '216.bg1', '216.bk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3470, -1, 4904, -1], 'generators': [10448, 7008, 15120], 'label': '17496.ro.72.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833270
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.h1'], 'contains': ['216.a1', '216.t1', '216.u1', '216.v1', '216.ba1', '216.bd1', '216.be1', '216.bf1', '216.bg2'], 'core': '216.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3773, -1, 4872, -1], 'generators': [5456, 15624, 15120], 'label': '17496.ro.72.br2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.br2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br2', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833271
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.f1', '24.g1'], 'contains': ['216.x1', '216.y1', '216.bb1', '216.bl1', '216.bo1', '216.bp1', '216.br1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1467, -1, 4283, -1], 'generators': [9512, 888, 7200], 'label': '17496.ro.72.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833272
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.f1', '24.g1'], 'contains': ['216.w1', '216.z1', '216.bc1', '216.bm1', '216.bp1', '216.bs1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2139, -1, 3996, -1], 'generators': [4976, 888, 7200], 'label': '17496.ro.72.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833273
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.g1'], 'contains': ['216.w1', '216.x1', '216.bb1', '216.bl1', '216.bm1', '216.bn1', '216.bq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1445, -1, 4346, -1], 'generators': [5408, 888, 15840], 'label': '17496.ro.72.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833274
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['24.b1', '36.a1', '36.c1', '36.f1', '36.h1', '36.j1', '36.l1', '36.n1', '36.o1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2216, -1, 6714, -1], 'generators': [9300, 648, 9288, 12320, 5832, 14712, 7200], 'label': '17496.ro.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '12.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833275
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.f1'], 'contains': ['216.y1', '216.z1', '216.bc1', '216.br1', '216.bs1', '216.bt1', '216.bv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2160, -1, 3932, -1], 'generators': [8000, 11040, 2880], 'label': '17496.ro.72.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833276
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1'], 'contains': ['216.cy1', '216.cz1', '216.da1', '216.db1', '216.dc1', '216.df1', '216.dj1', '216.dk1', '216.dl1', '216.ea1', '216.eb1', '216.ec1', '216.ed1', '216.eh1', '216.ek1', '216.eq1', '216.et1', '216.eu1', '216.ev1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [6943, -1, 1524, -1], 'generators': [12320, 14712, 15768, 14904], 'label': '17496.ro.72.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.bw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833277
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1'], 'contains': ['216.cy1', '216.da1', '216.db1', '216.de1', '216.dg1', '216.dj1', '216.dk1', '216.ea2', '216.ec2', '216.ed2', '216.ej1', '216.el1', '216.eq2', '216.et2', '216.eu2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [6651, -1, 1118, -1], 'generators': [12320, 8880, 15768, 14904], 'label': '17496.ro.72.bw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.bw2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833278
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bw3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1'], 'contains': ['216.cy1', '216.cz1', '216.db1', '216.dd1', '216.dh1', '216.dj1', '216.dl1', '216.ea3', '216.eb2', '216.ed3', '216.ei1', '216.em1', '216.eq3', '216.et3', '216.ev2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [6797, -1, 1320, -1], 'generators': [12320, 3048, 9936, 14904], 'label': '17496.ro.72.bw3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.bw3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833279
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '36.s1'], 'contains': ['216.dc1', '216.dd1', '216.de1', '216.df1', '216.dg1', '216.dh1', '216.di1', '216.ee1', '216.ef1', '216.eg1', '216.en1', '216.eo1', '216.ep1', '216.er1', '216.es1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [7703, -1, 2581, -1], 'generators': [12320, 14712, 9936, 14904], 'label': '17496.ro.72.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '72.bx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833280
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.e1'], 'contains': ['216.dm1', '216.dn1', '216.do1', '216.dp1', '216.dq1', '216.dt1', '216.dx1', '216.dy1', '216.dz1', '216.ea2', '216.ea3', '216.eb1', '216.eb2', '216.ec1', '216.ec2', '216.ed1', '216.ee1', '216.eh1', '216.ek1', '216.en1', '216.eq1', '216.et2', '216.et3', '216.eu1', '216.eu2', '216.ev1', '216.ev2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7036, -1, 977, -1], 'generators': [656, 14712, 15768, 14904], 'label': '17496.ro.72.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.by1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833281
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.by2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1'], 'contains': ['216.dm1', '216.do1', '216.dp1', '216.ds1', '216.du1', '216.dx1', '216.dy1', '216.ea1', '216.ea3', '216.ec1', '216.ed2', '216.eg1', '216.ej1', '216.el1', '216.eo1', '216.eq2', '216.et1', '216.et3', '216.eu1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7207, -1, 1178, -1], 'generators': [6488, 8880, 15768, 14904], 'label': '17496.ro.72.by2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.by2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833282
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.by3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1'], 'contains': ['216.dm1', '216.dn1', '216.dp1', '216.dr1', '216.dv1', '216.dx1', '216.dz1', '216.ea1', '216.ea2', '216.eb1', '216.ed3', '216.ef1', '216.ei1', '216.em1', '216.ep1', '216.eq3', '216.et1', '216.et2', '216.ev1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7376, -1, 1239, -1], 'generators': [6488, 14712, 7200, 15768], 'label': '17496.ro.72.by3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '72.by3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833283
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '36.t1'], 'contains': ['216.dq1', '216.dr1', '216.ds1', '216.dt1', '216.du1', '216.dv1', '216.dw1', '216.eh1', '216.ei1', '216.ej1', '216.ek1', '216.el1', '216.em1', '216.er1', '216.es1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7453, -1, 2520, -1], 'generators': [6488, 14712, 9936, 14904], 'label': '17496.ro.72.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '72.bz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833284
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['162.a1', '162.b1', '162.c1', '243.a1', '243.b1', '243.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [230, -1, 9542, -1], 'generators': [3469, 5832, 12320, 4914, 648, 9300], 'label': '17496.ro.81.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157833285
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['24.c1', '36.a1', '36.b1', '36.e1', '36.h1', '36.i1', '36.l1', '36.m1', '36.p1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1838, -1, 7279, -1], 'generators': [9300, 6480, 9936, 12320, 5832, 16008, 7200], 'label': '17496.ro.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '12.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833286
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['27.a1', '27.b1'], 'contains': ['162.f1', '162.g1', '162.h1', '729.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [1176, -1, 9913, -1], 'generators': [3469, 12312, 4392, 402, 9300, 15936], 'label': '17496.ro.81.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833287
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.d1', '36.e1', '36.f1', '36.g1'], 'contains': ['216.b1', '324.a1', '324.b1', '324.f1', '324.j1', '324.n1', '324.r1', '324.v1', '324.w1', '324.ba1', '324.bb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4182, -1, 7110, -1], 'generators': [9300, 14712, 12320, 648, 5832], 'label': '17496.ro.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '108.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833308
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1'], 'contains': ['216.bw1', '324.f1', '324.g1', '324.bf1', '324.bt1', '324.cd1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2995, -1, 7686, -1], 'generators': [9300, 16272, 12320, 12312, 14712], 'label': '17496.ro.108.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833288
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.d1', '36.h1', '36.i1', '36.j1', '36.k1', '36.k2'], 'contains': ['216.c1', '324.a1', '324.c1', '324.g1', '324.k1', '324.o1', '324.s1', '324.x1', '324.bc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2674, -1, 8426, -1], 'generators': [9300, 5928, 12320, 648, 5832], 'label': '17496.ro.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '108.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833289
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.b1', '36.e1', '36.h1', '36.i1', '36.l1', '36.m1'], 'contains': ['216.d1', '324.a1', '324.d1', '324.h1', '324.l1', '324.p1', '324.t1', '324.y1', '324.bd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [812, -1, 7893, -1], 'generators': [9300, 6720, 12320, 648, 5832], 'label': '17496.ro.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '108.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833290
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.c1', '36.f1', '36.h1', '36.j1', '36.l1', '36.n1'], 'contains': ['216.e1', '324.a1', '324.e1', '324.i1', '324.m1', '324.q1', '324.u1', '324.z1', '324.be1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1524, -1, 6008, -1], 'generators': [9300, 5208, 12320, 648, 5832], 'label': '17496.ro.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '108.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833291
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.a1', '36.o1', '36.p1', '36.q1', '36.r1'], 'contains': ['216.j1', '324.b1', '324.c1', '324.d1', '324.e1', '324.bw1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2904, -1, 6757, -1], 'generators': [9300, 6480, 5832, 16008, 7200], 'label': '17496.ro.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833292
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '36.p1', '36.q1', '36.r1'], 'contains': ['216.k1', '324.b1', '324.c1', '324.d1', '324.bx1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4376, -1, 7264, -1], 'generators': [9300, 648, 5832, 16008, 9936], 'label': '17496.ro.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833293
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.o1', '36.q1', '36.r1'], 'contains': ['216.l1', '324.b1', '324.c1', '324.e1', '324.by1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4806, -1, 6494, -1], 'generators': [9300, 648, 5832, 7008, 9936], 'label': '17496.ro.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '108.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833294
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.q1', '36.r1'], 'contains': ['216.p1', '324.b1', '324.c1', '324.bf1', '324.bm1', '324.bz1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3672, -1, 7317, -1], 'generators': [9300, 16272, 648, 5832, 14712], 'label': '17496.ro.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833295
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.p1', '36.r1', '54.a1'], 'contains': ['216.q1', '324.b1', '324.d1', '324.bg1', '324.bn1', '324.ca1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2642, -1, 7422, -1], 'generators': [5484, 2016, 648, 5832, 14712], 'label': '17496.ro.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833296
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['24.d1', '36.a1', '36.b1', '36.c1', '36.d1', '36.h1', '36.i1', '36.j1', '36.k1', '36.k2', '36.q1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2847, -1, 7351, -1], 'generators': [9300, 648, 9288, 12320, 5832, 14712, 16272], 'label': '17496.ro.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '12.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833297
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.o1', '36.r1', '54.b1'], 'contains': ['216.r1', '324.b1', '324.e1', '324.bh1', '324.bo1', '324.cb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3623, -1, 6388, -1], 'generators': [9300, 7200, 648, 5832, 14712], 'label': '17496.ro.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833298
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.r1', '54.c1'], 'contains': ['216.s1', '324.b1', '324.cc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6282, -1, 4590, -1], 'generators': [9300, 648, 5832, 14712, 9936], 'label': '17496.ro.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833299
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.h1', '36.o1', '36.p1', '36.q1'], 'contains': ['216.bh1', '324.c1', '324.d1', '324.e1', '324.bi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1492, -1, 7844, -1], 'generators': [9300, 12312, 5832, 2616, 2880], 'label': '17496.ro.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '108.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833300
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '36.p1', '36.q1'], 'contains': ['216.bi1', '324.c1', '324.d1', '324.bp1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2094, -1, 8099, -1], 'generators': [9300, 5832, 648, 16080, 6696], 'label': '17496.ro.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '108.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833301
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '36.o1', '36.q1'], 'contains': ['216.bj1', '324.c1', '324.e1', '324.bq1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2339, -1, 6956, -1], 'generators': [9300, 5832, 648, 5208, 7200], 'label': '17496.ro.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '108.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833302
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.q1'], 'contains': ['216.bk1', '324.c1', '324.br1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3087, -1, 8528, -1], 'generators': [9300, 5832, 648, 3744, 3240], 'label': '17496.ro.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '108.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833303
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.o2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.k2', '36.q1', '54.d1', '54.e1', '54.f1'], 'contains': ['216.a1', '324.c1', '324.bj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2297, -1, 9772, -1], 'generators': [9300, 12312, 5832, 5928, 3240], 'label': '17496.ro.108.o2', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.o2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o2', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833304
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '36.o1', '36.p1', '54.g1'], 'contains': ['216.bp1', '324.d1', '324.e1', '324.bs1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [696, -1, 6851, -1], 'generators': [9300, 5832, 648, 6720, 7200], 'label': '17496.ro.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '108.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833305
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.p1', '54.h1'], 'contains': ['216.bq1', '324.d1', '324.bk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [304, -1, 7941, -1], 'generators': [1956, 12312, 5832, 7728, 6696], 'label': '17496.ro.108.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '108.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833306
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.o1', '54.i1'], 'contains': ['216.bv1', '324.e1', '324.bl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1414, -1, 5615, -1], 'generators': [8724, 12312, 5832, 13848, 7200], 'label': '17496.ro.108.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833307
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['24.e1', '36.a1', '36.b1', '36.c1', '36.d1', '36.e1', '36.f1', '36.g1', '36.r1', '36.s1', '36.t1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4547, -1, 6524, -1], 'generators': [9300, 3240, 9936, 12320, 648, 5832, 14712], 'label': '17496.ro.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '12.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833309
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '54.j1'], 'contains': ['216.bx1', '324.f1', '324.h1', '324.bg1', '324.bu1', '324.ce1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2129, -1, 7791, -1], 'generators': [5484, 2016, 12312, 12320, 14712], 'label': '17496.ro.108.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833310
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '54.k1'], 'contains': ['216.by1', '324.f1', '324.i1', '324.bh1', '324.bv1', '324.cf1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2764, -1, 6336, -1], 'generators': [3900, 9936, 12320, 12312, 13416], 'label': '17496.ro.108.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833311
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.h1'], 'contains': ['216.bz1', '324.g1', '324.h1', '324.i1', '324.bi1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1456, -1, 8047, -1], 'generators': [9300, 12312, 12320, 5208, 16272], 'label': '17496.ro.108.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '108.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833312
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.k2', '54.l1', '54.m1', '54.n1'], 'contains': ['216.ca1', '324.g1', '324.bj1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2263, -1, 9544, -1], 'generators': [9300, 12312, 12320, 16272, 9288], 'label': '17496.ro.108.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833313
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '54.o1'], 'contains': ['216.cb1', '324.h1', '324.bk1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [61, -1, 8325, -1], 'generators': [1956, 12312, 12320, 7728, 6696], 'label': '17496.ro.108.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '108.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833314
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '54.p1'], 'contains': ['216.cc1', '324.i1', '324.bl1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [1379, -1, 5562, -1], 'generators': [5052, 12312, 12320, 10392, 2880], 'label': '17496.ro.108.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833315
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1'], 'contains': ['216.cd1', '324.j1', '324.k1', '324.bf1', '324.cg1', '324.cj1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3362, -1, 7528, -1], 'generators': [9300, 16272, 6488, 12312, 14712], 'label': '17496.ro.108.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833316
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.e1', '54.q1'], 'contains': ['216.ce1', '324.j1', '324.l1', '324.bg1', '324.ch1', '324.ck1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2573, -1, 7633, -1], 'generators': [5484, 2016, 12312, 6488, 14712], 'label': '17496.ro.108.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833317
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1'], 'contains': ['216.cf1', '324.j1', '324.m1', '324.bh1', '324.ci1', '324.cl1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3459, -1, 5960, -1], 'generators': [9300, 7200, 656, 12312, 14712], 'label': '17496.ro.108.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '108.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833318
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['36.e1', '54.a1', '54.j1', '54.q1', '54.t1', '162.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [647, -1, 9005, -1], 'generators': [8155, 9144, 10896, 648, 5832, 8100, 12320], 'label': '17496.ro.18.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '18.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '324.163'}
  • id: 157833319
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.h1'], 'contains': ['216.cg1', '324.k1', '324.l1', '324.m1', '324.bi1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1732, -1, 7994, -1], 'generators': [9300, 12312, 6488, 5208, 16272], 'label': '17496.ro.108.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '108.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833320
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.k2', '54.r1'], 'contains': ['216.ch1', '324.k1', '324.bj1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2607, -1, 9311, -1], 'generators': [9300, 12312, 656, 2616, 16704], 'label': '17496.ro.108.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '108.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833321
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1'], 'contains': ['216.ci1', '324.l1', '324.bk1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [139, -1, 8152, -1], 'generators': [1956, 12312, 656, 7728, 6696], 'label': '17496.ro.108.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '108.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833322
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.n1', '54.s1'], 'contains': ['216.cj1', '324.m1', '324.bl1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1634, -1, 5510, -1], 'generators': [5052, 12312, 6488, 10392, 2880], 'label': '17496.ro.108.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833323
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1'], 'contains': ['216.ck1', '324.n1', '324.o1', '324.bm1', '324.bt1', '324.cg1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [3031, -1, 7580, -1], 'generators': [9300, 16272, 12320, 5832, 14712], 'label': '17496.ro.108.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.bg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833324
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '54.t1'], 'contains': ['216.cl1', '324.n1', '324.p1', '324.bn1', '324.bu1', '324.ch1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [2199, -1, 7739, -1], 'generators': [5484, 2016, 12320, 5832, 14712], 'label': '17496.ro.108.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.bh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833325
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '54.u1'], 'contains': ['216.cm1', '324.n1', '324.q1', '324.bo1', '324.bv1', '324.ci1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [2812, -1, 6283, -1], 'generators': [9300, 7200, 12320, 5832, 14712], 'label': '17496.ro.108.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.bi1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833326
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1'], 'contains': ['216.cn1', '324.o1', '324.p1', '324.bp1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [2010, -1, 8475, -1], 'generators': [9300, 5832, 12320, 6720, 6768], 'label': '17496.ro.108.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '108.bj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833327
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1'], 'contains': ['216.co1', '324.o1', '324.q1', '324.bq1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [2537, -1, 7061, -1], 'generators': [9300, 5832, 12320, 5208, 7200], 'label': '17496.ro.108.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '108.bk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833328
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1'], 'contains': ['216.cp1', '324.o1', '324.br1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [3121, -1, 8633, -1], 'generators': [9300, 5832, 12320, 3744, 3240], 'label': '17496.ro.108.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '108.bl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833329
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['36.f1', '54.b1', '54.k1', '54.u1', '54.w1', '162.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [759, -1, 8834, -1], 'generators': [6, 4752, 8016, 12320, 5832, 648, 12], 'label': '17496.ro.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '18.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833330
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.v1'], 'contains': ['216.cq1', '324.p1', '324.q1', '324.bs1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [780, -1, 6903, -1], 'generators': [9300, 5832, 12320, 6720, 7200], 'label': '17496.ro.108.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '108.bm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833331
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1'], 'contains': ['216.cr1', '324.r1', '324.s1', '324.bm1', '324.cd1', '324.cj1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3227, -1, 7475, -1], 'generators': [9300, 16272, 11672, 5832, 14712], 'label': '17496.ro.108.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.bn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833332
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1'], 'contains': ['216.cs1', '324.r1', '324.t1', '324.bn1', '324.ce1', '324.ck1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2855, -1, 7369, -1], 'generators': [5484, 2016, 12968, 5832, 14712], 'label': '17496.ro.108.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '108.bo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833333
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '54.w1'], 'contains': ['216.ct1', '324.r1', '324.u1', '324.bo1', '324.cf1', '324.cl1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3418, -1, 6230, -1], 'generators': [3900, 9936, 11672, 5832, 13416], 'label': '17496.ro.108.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.bp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833334
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1'], 'contains': ['216.cu1', '324.s1', '324.t1', '324.bp1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [2051, -1, 8378, -1], 'generators': [9300, 5832, 11672, 6720, 6768], 'label': '17496.ro.108.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '108.bq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833335
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.j1'], 'contains': ['216.cv1', '324.s1', '324.u1', '324.bq1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [2502, -1, 7009, -1], 'generators': [9300, 5832, 11672, 7200, 9288], 'label': '17496.ro.108.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '108.br1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.br1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833336
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1'], 'contains': ['216.cw1', '324.s1', '324.br1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3157, -1, 8580, -1], 'generators': [9300, 5832, 11672, 3744, 3240], 'label': '17496.ro.108.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '108.bs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bs1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833337
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1'], 'contains': ['216.cx1', '324.t1', '324.u1', '324.bs1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [949, -1, 6705, -1], 'generators': [9300, 5832, 12968, 6720, 7200], 'label': '17496.ro.108.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '108.bt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bt1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833338
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.a1', '36.s1'], 'contains': ['216.dc1', '324.w1', '324.x1', '324.y1', '324.z1', '324.bw1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 288, 'diagramx': [4608, -1, 5802, -1], 'generators': [9300, 648, 12320, 24, 7200], 'label': '17496.ro.108.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.bu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bu1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833339
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '36.s1'], 'contains': ['216.dd1', '324.w1', '324.x1', '324.y1', '324.bx1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [4573, -1, 6057, -1], 'generators': [9300, 648, 12320, 14712, 16488], 'label': '17496.ro.108.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.bv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833340
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['36.g1', '54.c1', '54.x1', '162.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4224, -1, 6868, -1], 'generators': [3469, 10584, 14712, 5832, 648, 9300, 12320], 'label': '17496.ro.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '18.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833341
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.s1'], 'contains': ['216.de1', '324.w1', '324.x1', '324.z1', '324.by1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [4926, -1, 5668, -1], 'generators': [9300, 648, 12320, 14712, 6768], 'label': '17496.ro.108.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '108.bw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bw1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833342
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1', '36.s1'], 'contains': ['216.df1', '324.v1', '324.w1', '324.x1', '324.bt1', '324.bz1', '324.cj1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [4503, -1, 6546, -1], 'generators': [9300, 16272, 12320, 6480, 14712], 'label': '17496.ro.108.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.bx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bx1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833343
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '36.s1'], 'contains': ['216.dg1', '324.v1', '324.w1', '324.y1', '324.bu1', '324.ca1', '324.ck1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [4057, -1, 6599, -1], 'generators': [5484, 2016, 648, 12320, 14712], 'label': '17496.ro.108.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '108.by1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833344
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.s1'], 'contains': ['216.dh1', '324.v1', '324.w1', '324.z1', '324.bv1', '324.cb1', '324.cl1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [4537, -1, 5749, -1], 'generators': [9300, 7200, 12320, 648, 14712], 'label': '17496.ro.108.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '108.bz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833345
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.s1', '54.x1'], 'contains': ['216.di1', '324.w1', '324.cc1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [6514, -1, 4484, -1], 'generators': [9300, 648, 12320, 14712, 9936], 'label': '17496.ro.108.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.ca1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833346
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['36.a1', '36.t1'], 'contains': ['216.dq1', '324.bb1', '324.bc1', '324.bd1', '324.be1', '324.bw1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [4433, -1, 6441, -1], 'generators': [9300, 648, 6488, 24, 7200], 'label': '17496.ro.108.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.cb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833347
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.b1', '36.t1'], 'contains': ['216.dr1', '324.bb1', '324.bc1', '324.bd1', '324.bx1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4468, -1, 6652, -1], 'generators': [9300, 648, 6488, 14712, 16488], 'label': '17496.ro.108.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.cc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833348
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.c1', '36.t1'], 'contains': ['216.ds1', '324.bb1', '324.bc1', '324.be1', '324.by1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4891, -1, 5855, -1], 'generators': [9300, 648, 6488, 14712, 6768], 'label': '17496.ro.108.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '108.cd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833349
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.d1', '36.t1'], 'contains': ['216.dt1', '324.ba1', '324.bb1', '324.bc1', '324.bz1', '324.cd1', '324.cg1', '324.cj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4293, -1, 7211, -1], 'generators': [9300, 16272, 6488, 6480, 14712], 'label': '17496.ro.108.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '108.ce1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833350
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.e1', '36.t1'], 'contains': ['216.du1', '324.ba1', '324.bb1', '324.bd1', '324.ca1', '324.ce1', '324.ch1', '324.ck1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3844, -1, 7158, -1], 'generators': [5484, 2016, 648, 6488, 14712], 'label': '17496.ro.108.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '108.cf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833351
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.b1', '18.c1', '18.d1', '18.g1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1237, 1201, 8619, 738], 'generators': [3469, 5832, 7848, 10584, 9300, 14712, 648, 14256, 12320], 'label': '17496.ro.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '1944.3931'}
  • id: 157833352
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.k2', '54.d1', '54.l1', '162.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1233, -1, 9511, -1], 'generators': [3469, 13608, 9168, 5832, 12312, 9300, 12320], 'label': '17496.ro.18.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833353
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '36.t1'], 'contains': ['216.dv1', '324.ba1', '324.bb1', '324.be1', '324.cb1', '324.cf1', '324.ci1', '324.cl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4327, -1, 5907, -1], 'generators': [9300, 7200, 6488, 648, 14712], 'label': '17496.ro.108.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '108.cg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833354
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.t1'], 'contains': ['216.dw1', '324.bb1', '324.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6459, -1, 4537, -1], 'generators': [9300, 648, 656, 14712, 9936], 'label': '17496.ro.108.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '108.ch1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833355
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '108.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '36.s1', '36.t1'], 'contains': ['216.es1', '324.bw1', '324.bx1', '324.by1', '324.bz1', '324.ca1', '324.cb1', '324.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5336, -1, 5709, -1], 'generators': [9300, 648, 14712, 7200, 9936], 'label': '17496.ro.108.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '108.ci1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ci1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833356
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '18.d1', '18.g1', '81.a1'], 'contains': ['324.a1', '486.a1', '486.d1', '486.h1', '486.l1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [450, -1, 9427, -1], 'generators': [3469, 12320, 648, 5832, 9300], 'label': '17496.ro.162.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833357
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.e1', '18.h1', '81.a1'], 'contains': ['324.a1', '486.b1', '486.e1', '486.i1', '486.k1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [224, -1, 9491, -1], 'generators': [6, 5832, 12320, 648, 12], 'label': '17496.ro.162.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833358
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.f1', '18.i1', '81.a1'], 'contains': ['324.a1', '486.c1', '486.f1', '486.g1', '486.j1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [274, -1, 9374, -1], 'generators': [4255, 5832, 648, 17292, 12320], 'label': '17496.ro.162.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157833359
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.j1', '54.q1'], 'contains': ['324.bg1', '486.m1', '1458.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [534, -1, 9195, -1], 'generators': [8155, 14976, 12312, 8100, 10896], 'label': '17496.ro.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.d1', 'old_label': '162.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833360
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.k1'], 'contains': ['324.bh1', '486.n1', '1458.b1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [992, -1, 8933, -1], 'generators': [6, 10584, 12312, 12, 8016], 'label': '17496.ro.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '162.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833361
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.d1', '54.l1', '81.b1'], 'contains': ['324.bj1', '1458.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1231, -1, 9870, -1], 'generators': [3469, 12312, 9300, 2040, 13608], 'label': '17496.ro.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833362
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.e1', '54.m1', '81.b1'], 'contains': ['324.bj1', '1458.b1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1149, -1, 9968, -1], 'generators': [6, 12312, 12, 4632, 14256], 'label': '17496.ro.162.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833363
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '9.a1'], 'contains': ['36.k2', '54.e1', '54.m1', '162.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [883, -1, 9598, -1], 'generators': [6, 5832, 10224, 12320, 12312, 12, 17232], 'label': '17496.ro.18.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833364
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.f1', '54.n1', '54.r1', '81.b1'], 'contains': ['324.bj1', '1458.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [1205, -1, 9818, -1], 'generators': [4255, 12312, 17292, 11400, 16056], 'label': '17496.ro.162.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833365
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1', '54.o1'], 'contains': ['324.bk1', '1458.b1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [12, -1, 9264, -1], 'generators': [6, 12312, 12, 12264, 13176], 'label': '17496.ro.162.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '162.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833366
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1', '54.p1', '54.s1'], 'contains': ['324.bl1', '1458.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [334, -1, 8690, -1], 'generators': [12691, 12312, 8196, 15216, 1368], 'label': '17496.ro.162.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.j1', 'old_label': '162.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833367
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.t1'], 'contains': ['324.bn1', '486.m1', '1458.f1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [568, -1, 9091, -1], 'generators': [16723, 5832, 4884, 13344, 5400], 'label': '17496.ro.162.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '162.k1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833368
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.u1', '54.w1'], 'contains': ['324.bo1', '486.n1', '1458.e1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1063, -1, 8884, -1], 'generators': [6, 5832, 12, 8016, 10584], 'label': '17496.ro.162.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '162.l1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833369
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.g1', '54.v1'], 'contains': ['324.bs1', '1458.d1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [488, -1, 8731, -1], 'generators': [3469, 5832, 9300, 6720, 13032], 'label': '17496.ro.162.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '162.m1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833370
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.j1', '54.t1'], 'contains': ['324.bu1', '486.m1', '1458.i1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 108, 'diagramx': [732, -1, 9026, -1], 'generators': [11623, 7344, 10620, 12320, 672], 'label': '17496.ro.162.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '162.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833371
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.k1', '54.u1'], 'contains': ['324.bv1', '486.n1', '1458.h1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 108, 'diagramx': [1030, -1, 8834, -1], 'generators': [6, 10584, 12320, 12, 8016], 'label': '17496.ro.162.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '162.o1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833372
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.x1'], 'contains': ['324.cc1', '1458.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4117, -1, 6804, -1], 'generators': [3469, 648, 9300, 14712, 10584], 'label': '17496.ro.162.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1', 'old_label': '162.p1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.p1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833373
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.k1', '54.w1'], 'contains': ['324.cf1', '486.n1', '1458.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1110, -1, 8779, -1], 'generators': [6, 10584, 7136, 12, 8016], 'label': '17496.ro.162.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '162.q1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833374
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '9.a1'], 'contains': ['36.k2', '54.f1', '54.n1', '54.r1', '162.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1073, -1, 9432, -1], 'generators': [4255, 5832, 12816, 17292, 12312, 12320, 5640], 'label': '17496.ro.18.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
  • id: 157833375
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '162.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.q1', '54.t1'], 'contains': ['324.ch1', '486.m1', '1458.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [704, -1, 8983, -1], 'generators': [11623, 7344, 10620, 656, 672], 'label': '17496.ro.162.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '162.r1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.r1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833376
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.bf1', '72.br2', '108.o2'], 'contains': ['648.d1', '648.bd1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2599, 7517, 8456, 6623], 'generators': [13632, 17352, 5832], 'label': '17496.ro.216.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['24.a1', '72.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157833377
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.c1', '72.d1', '72.e1', '72.f1', '72.g1', '72.h1', '108.a1'], 'contains': ['648.a1', '648.b1', '648.c1', '648.j1', '648.n1', '648.bk1', '648.bo1', '648.cm1', '648.cn1', '648.co1', '648.db1', '648.dc1', '648.dd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5700, -1, 3334, -1], 'generators': [12320, 15360, 648, 5832], 'label': '17496.ro.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833378
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.d1', '72.e1', '72.i1', '72.j1', '72.k1', '72.l1', '108.b1'], 'contains': ['648.a1', '648.d1', '648.g1', '648.k1', '648.o1', '648.bl1', '648.bp1', '648.cp1', '648.de1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3473, -1, 6527, -1], 'generators': [12320, 15864, 648, 5832], 'label': '17496.ro.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833379
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.c1', '72.f1', '72.i1', '72.j1', '72.m1', '72.n1', '108.c1'], 'contains': ['648.a1', '648.e1', '648.h1', '648.l1', '648.p1', '648.bm1', '648.bq1', '648.cq1', '648.df1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [996, -1, 5169, -1], 'generators': [12320, 888, 648, 5832], 'label': '17496.ro.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833380
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.d1', '72.g1', '72.i1', '72.k1', '72.m1', '72.o1', '108.d1'], 'contains': ['648.a1', '648.f1', '648.i1', '648.m1', '648.q1', '648.bn1', '648.br1', '648.cr1', '648.dg1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2315, -1, 4391, -1], 'generators': [12320, 7200, 648, 5832], 'label': '17496.ro.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833381
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.r1', '72.t1', '72.v1', '72.w1', '72.z1', '72.ba1', '72.bb1', '72.bi1'], 'contains': ['648.b1', '648.c1', '648.g1', '648.r1', '648.bs1', '648.dh1', '648.dk1', '648.dr1', '648.eg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6586, -1, 3187, -1], 'generators': [10448, 15360, 648, 5832], 'label': '17496.ro.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833382
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.q1', '72.s1', '72.y1', '72.z1', '72.bb1', '72.bi1'], 'contains': ['648.b1', '648.c1', '648.h1', '648.s1', '648.bt1', '648.di1', '648.dl1', '648.ds1', '648.eh1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5304, -1, 3048, -1], 'generators': [15704, 15360, 648, 5832], 'label': '17496.ro.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833383
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.p1', '72.u1', '72.x1', '72.z1', '72.ba1', '72.bi1'], 'contains': ['648.b1', '648.c1', '648.i1', '648.t1', '648.bu1', '648.dj1', '648.dm1', '648.dt1', '648.ei1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6189, -1, 2932, -1], 'generators': [7280, 15360, 648, 5832], 'label': '17496.ro.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833384
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '72.w1', '72.x1', '72.y1', '72.z1', '72.ba1', '72.bb1'], 'contains': ['648.b1', '648.c1', '648.du1', '648.dv1', '648.ej1', '648.ej2'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8438, -1, 1603, -1], 'generators': [5456, 10584, 5832], 'label': '17496.ro.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833385
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['36.l1', '54.g1', '54.v1', '162.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [518, -1, 8594, -1], 'generators': [3469, 14544, 11832, 648, 5832, 9300, 12320], 'label': '17496.ro.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '18.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833386
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.p1', '72.q1', '72.r1', '72.w1', '72.bd1', '72.be1', '72.bf1', '72.bj1', '108.e1'], 'contains': ['648.b1', '648.d1', '648.e1', '648.f1', '648.dw1', '648.ek1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3602, -1, 3933, -1], 'generators': [15360, 15120, 5832], 'label': '17496.ro.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833387
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.s1', '72.t1', '72.x1', '72.be1', '72.bf1', '72.bj1', '108.f1'], 'contains': ['648.b1', '648.d1', '648.e1', '648.dx1', '648.el1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4949, -1, 3987, -1], 'generators': [10824, 10584, 5832], 'label': '17496.ro.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833388
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.u1', '72.v1', '72.y1', '72.bd1', '72.bf1', '72.bj1', '108.g1'], 'contains': ['648.b1', '648.d1', '648.f1', '648.dy1', '648.em1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5036, -1, 3777, -1], 'generators': [15360, 7416, 5832], 'label': '17496.ro.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833389
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.p1', '72.q1', '72.s1', '72.t1', '72.u1', '72.v1', '72.w1', '72.z1', '72.bc1', '72.bg1', '72.bh1', '72.bi1'], 'contains': ['648.b1', '648.g1', '648.h1', '648.i1', '648.dz1', '648.en1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3874, -1, 3482, -1], 'generators': [7280, 4488, 5832], 'label': '17496.ro.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833390
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.q1', '72.r1', '72.v1', '72.x1', '72.bb1', '72.bc1', '72.bg1', '72.bi1'], 'contains': ['648.b1', '648.g1', '648.h1', '648.ea1', '648.eo1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5074, -1, 3373, -1], 'generators': [2528, 15360, 5832], 'label': '17496.ro.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833391
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.p1', '72.r1', '72.t1', '72.y1', '72.ba1', '72.bc1', '72.bh1', '72.bi1'], 'contains': ['648.b1', '648.g1', '648.i1', '648.eb1', '648.ep1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5230, -1, 3225, -1], 'generators': [7064, 15360, 5832], 'label': '17496.ro.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833392
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.z1', '72.bc1', '72.bf1', '72.bj1', '108.h1'], 'contains': ['648.b1', '648.d1', '648.u1', '648.bv1', '648.dn1', '648.ec1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5521, -1, 4764, -1], 'generators': [15360, 15624, 648, 5832], 'label': '17496.ro.216.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833393
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.ba1', '72.be1', '72.bg1', '72.bj1', '108.i1'], 'contains': ['648.b1', '648.e1', '648.v1', '648.bw1', '648.do1', '648.ed1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3132, -1, 3894, -1], 'generators': [15360, 2664, 648, 5832], 'label': '17496.ro.216.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '216.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833394
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.bb1', '72.bd1', '72.bh1', '72.bj1', '108.j1'], 'contains': ['648.b1', '648.f1', '648.w1', '648.bx1', '648.dp1', '648.ee1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4398, -1, 3311, -1], 'generators': [456, 10584, 648, 5832], 'label': '17496.ro.216.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833395
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.bi1', '72.bj1', '108.k1'], 'contains': ['648.b1', '648.dq1', '648.ef1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7150, -1, 2792, -1], 'generators': [15360, 10584, 5832], 'label': '17496.ro.216.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833396
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['36.m1', '54.h1', '54.o1', '162.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [147, -1, 9243, -1], 'generators': [6, 5832, 7344, 12320, 12312, 12, 12264], 'label': '17496.ro.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '18.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833397
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.q1', '72.t1', '72.v1', '72.w1', '72.y1', '72.z1', '72.bl1', '72.bm1', '72.bn1', '72.bq1', '72.br1', '72.br2'], 'contains': ['648.c1', '648.d1', '648.g1', '648.h1', '648.et1', '648.fd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5445, -1, 4329, -1], 'generators': [5456, 2448, 5832], 'label': '17496.ro.216.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833398
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.p1', '72.t1', '72.v1', '72.w1', '72.x1', '72.z1', '72.bk1', '72.bm1', '72.bo1', '72.bp1', '72.br1', '72.br2'], 'contains': ['648.c1', '648.d1', '648.g1', '648.i1', '648.eu1', '648.fe1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4985, -1, 3855, -1], 'generators': [296, 2688, 5832], 'label': '17496.ro.216.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833399
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.r1', '72.s1', '72.u1', '72.x1', '72.y1', '72.z1', '72.bk1', '72.bl1', '72.bn1', '72.bp1', '72.br1', '72.br2'], 'contains': ['648.c1', '648.d1', '648.h1', '648.i1', '648.ev1', '648.ff1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4913, -1, 3590, -1], 'generators': [7280, 10824, 5832], 'label': '17496.ro.216.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833400
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.p1', '72.q1', '72.t1', '72.w1', '72.x1', '72.ba1', '72.bk1', '72.bm1', '72.bn1', '72.bo1', '72.bt1', '72.bu1'], 'contains': ['648.c1', '648.e1', '648.g1', '648.i1', '648.ew1', '648.fg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5482, -1, 3645, -1], 'generators': [80, 17376, 5832], 'label': '17496.ro.216.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833401
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.r1', '72.s1', '72.w1', '72.ba1', '72.bm1', '72.bo1', '72.bs1', '72.bu1'], 'contains': ['648.c1', '648.e1', '648.g1', '648.ex1', '648.fh1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6523, -1, 3699, -1], 'generators': [5456, 15840, 5832], 'label': '17496.ro.216.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833402
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.p1', '72.q1', '72.v1', '72.w1', '72.y1', '72.bb1', '72.bl1', '72.bm1', '72.bp1', '72.bq1', '72.bs1', '72.bv1'], 'contains': ['648.c1', '648.f1', '648.g1', '648.h1', '648.ey1', '648.fi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5138, -1, 3536, -1], 'generators': [8048, 7200, 5832], 'label': '17496.ro.216.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833403
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.r1', '72.u1', '72.w1', '72.bb1', '72.bm1', '72.bq1', '72.bt1', '72.bv1'], 'contains': ['648.c1', '648.f1', '648.g1', '648.ez1', '648.fj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6560, -1, 3427, -1], 'generators': [7064, 9456, 5832], 'label': '17496.ro.216.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157833404
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.w1', '72.x1', '72.y1', '72.bm1', '72.bo1', '72.bq1', '72.br1', '72.br2'], 'contains': ['648.c1', '648.d1', '648.g1', '648.x1', '648.by1', '648.eq1', '648.fa1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5886, -1, 4741, -1], 'generators': [5456, 14904, 648, 5832], 'label': '17496.ro.216.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833405
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.w1', '72.x1', '72.bl1', '72.bn1', '72.bs1', '72.bu1'], 'contains': ['648.c1', '648.e1', '648.h1', '648.y1', '648.bz1', '648.er1', '648.fb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1269, -1, 3738, -1], 'generators': [9512, 12048, 648, 5832], 'label': '17496.ro.216.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833406
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.w1', '72.y1', '72.bk1', '72.bp1', '72.bt1', '72.bv1'], 'contains': ['648.c1', '648.f1', '648.i1', '648.z1', '648.ca1', '648.es1', '648.fc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3823, -1, 3117, -1], 'generators': [5456, 7200, 648, 5832], 'label': '17496.ro.216.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833407
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['36.n1', '54.i1', '54.p1', '54.s1', '162.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [383, -1, 8476, -1], 'generators': [8371, 5832, 8712, 9204, 12312, 12320, 15504], 'label': '17496.ro.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '18.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '324.163'}
  • id: 157833408
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.i1', '72.p1', '72.q1', '72.s1', '72.t1', '72.u1', '72.v1', '72.bc1', '72.bm1', '72.bn1', '72.bp1', '72.br1', '72.br2'], 'contains': ['648.d1', '648.g1', '648.h1', '648.i1', '648.ba1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2416, -1, 4593, -1], 'generators': [7280, 13632, 5832], 'label': '17496.ro.216.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833409
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.j1', '72.q1', '72.s1', '72.v1', '72.bc1', '72.bl1', '72.bq1', '72.br1', '72.br2'], 'contains': ['648.d1', '648.g1', '648.h1', '648.cb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3418, -1, 5208, -1], 'generators': [12536, 15648, 648], 'label': '17496.ro.216.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833410
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.k1', '72.p1', '72.t1', '72.u1', '72.bc1', '72.bk1', '72.bo1', '72.br1', '72.br2'], 'contains': ['648.d1', '648.g1', '648.i1', '648.cc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3232, -1, 4858, -1], 'generators': [80, 4704, 648], 'label': '17496.ro.216.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833411
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.r1', '72.t1', '72.v1', '72.bc1', '72.bm1', '72.bo1', '72.bq1', '72.br1'], 'contains': ['648.d1', '648.g1', '648.bb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2843, -1, 6241, -1], 'generators': [5192, 7224, 5832], 'label': '17496.ro.216.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833412
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.l1', '72.r1', '72.t1', '72.v1', '72.bc1', '72.bm1', '72.bo1', '72.bq1', '72.br2'], 'contains': ['648.d1', '648.g1', '648.cd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3638, -1, 6187, -1], 'generators': [5192, 6984, 648], 'label': '17496.ro.216.bg2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bg2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg2', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833413
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.i1', '72.bd1', '72.be1', '72.bf1', '72.bk1', '72.bl1', '72.bm1', '108.l1'], 'contains': ['648.d1', '648.e1', '648.f1', '648.bc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1468, -1, 5262, -1], 'generators': [13848, 2448, 5832], 'label': '17496.ro.216.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833414
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.be1', '72.bf1', '72.bn1', '72.bo1', '108.m1'], 'contains': ['648.d1', '648.e1', '648.ce1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2002, -1, 6296, -1], 'generators': [17376, 216, 648], 'label': '17496.ro.216.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833415
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.bd1', '72.bf1', '72.bp1', '72.bq1', '108.n1'], 'contains': ['648.d1', '648.f1', '648.cf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2563, -1, 5316, -1], 'generators': [11040, 7200, 648], 'label': '17496.ro.216.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833416
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.bf1', '72.br1', '108.o1'], 'contains': ['648.d1', '648.cg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3342, -1, 8401, -1], 'generators': [2448, 14904, 648], 'label': '17496.ro.216.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833417
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.j1', '72.q1', '72.r1', '72.t1', '72.bg1', '72.bm1', '72.bn1', '72.bs1', '72.bu1'], 'contains': ['648.e1', '648.g1', '648.h1', '648.ch1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [864, -1, 4702, -1], 'generators': [10256, 216, 648], 'label': '17496.ro.216.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833418
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': ['729.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1'], 'contains': ['72.bd1', '72.be1', '72.bf1', '72.bj1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2752, 4688, 4492, 3347], 'generators': [15360, 7200, 10584, 14904], 'label': '17496.ro.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': None, 'quotient_action_image': '8.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157833419
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.i1', '72.p1', '72.r1', '72.t1', '72.bg1', '72.bl1', '72.bo1', '72.bt1', '72.bu1'], 'contains': ['648.e1', '648.g1', '648.i1', '648.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1778, -1, 4539, -1], 'generators': [7280, 9240, 5832], 'label': '17496.ro.216.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833420
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '72.p1', '72.s1', '72.bg1', '72.bk1', '72.bn1', '72.bu1'], 'contains': ['648.e1', '648.h1', '648.i1', '648.ci1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1244, -1, 4485, -1], 'generators': [7280, 888, 648], 'label': '17496.ro.216.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833421
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.n1', '72.q1', '72.s1', '72.bg1', '72.bl1', '72.bn1', '72.bs1'], 'contains': ['648.e1', '648.h1', '648.bf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [628, -1, 4648, -1], 'generators': [12536, 12048, 5832], 'label': '17496.ro.216.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833422
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '72.bd1', '72.be1', '72.bs1', '72.bt1', '108.p1'], 'contains': ['648.e1', '648.f1', '648.cj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [827, -1, 4912, -1], 'generators': [13848, 2880, 648], 'label': '17496.ro.216.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157833423
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '72.be1', '72.bu1', '108.q1'], 'contains': ['648.e1', '648.bg1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [423, -1, 5525, -1], 'generators': [13560, 216, 5832], 'label': '17496.ro.216.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157833424
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.i1', '72.q1', '72.r1', '72.v1', '72.bh1', '72.bk1', '72.bq1', '72.bs1', '72.bv1'], 'contains': ['648.f1', '648.g1', '648.h1', '648.bh1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1424, -1, 4430, -1], 'generators': [5240, 7200, 5832], 'label': '17496.ro.216.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833425
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.k1', '72.p1', '72.r1', '72.v1', '72.bh1', '72.bm1', '72.bp1', '72.bt1', '72.bv1'], 'contains': ['648.f1', '648.g1', '648.i1', '648.ck1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1850, -1, 4275, -1], 'generators': [3920, 7200, 648], 'label': '17496.ro.216.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833426
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '72.q1', '72.u1', '72.bh1', '72.bl1', '72.bp1', '72.bv1'], 'contains': ['648.f1', '648.h1', '648.i1', '648.cl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1814, -1, 4220, -1], 'generators': [12152, 7200, 648], 'label': '17496.ro.216.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833427
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '72.p1', '72.u1', '72.bh1', '72.bk1', '72.bp1', '72.bt1'], 'contains': ['648.f1', '648.i1', '648.bi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1741, -1, 4166, -1], 'generators': [8672, 7200, 5832], 'label': '17496.ro.216.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833428
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.bd1', '72.bv1', '108.r1'], 'contains': ['648.f1', '648.bj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1388, -1, 4803, -1], 'generators': [13848, 7200, 5832], 'label': '17496.ro.216.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '216.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157833429
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.b1'], 'contains': ['72.b1', '72.d1', '72.g1', '72.i1', '72.k1', '72.m1', '72.o1', '72.p1', '72.u1', '72.bd1', '72.bh1', '72.bk1', '72.bp1', '72.bt1', '72.bv1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2659, -1, 4105, -1], 'generators': [12320, 15360, 7200, 15120], 'label': '17496.ro.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833430
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.s1'], 'contains': ['648.j1', '648.k1', '648.r1', '648.u1', '648.x1', '648.cs1', '648.cv1', '648.cy1', '648.fk1', '648.fn1', '648.fq1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [5562, -1, 6148, -1], 'generators': [12320, 3048, 15624, 12312], 'label': '17496.ro.216.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '216.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833431
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '108.t1'], 'contains': ['648.j1', '648.l1', '648.s1', '648.v1', '648.y1', '648.ct1', '648.cw1', '648.cz1', '648.fl1', '648.fo1', '648.fr1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2149, -1, 4127, -1], 'generators': [12320, 8232, 7848, 12312], 'label': '17496.ro.216.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833432
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '108.u1'], 'contains': ['648.j1', '648.m1', '648.t1', '648.w1', '648.z1', '648.cu1', '648.cx1', '648.da1', '648.fm1', '648.fp1', '648.fs1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3987, -1, 3287, -1], 'generators': [12320, 12768, 15768, 12312], 'label': '17496.ro.216.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833433
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.i1', '108.v1'], 'contains': ['648.k1', '648.l1', '648.m1', '648.ba1', '648.bc1', '648.be1', '648.bh1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1641, -1, 7116, -1], 'generators': [12320, 3912, 15624], 'label': '17496.ro.216.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '216.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833434
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '108.w1'], 'contains': ['648.k1', '648.bb1', '648.bd1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2721, -1, 9122, -1], 'generators': [12320, 7224, 14904], 'label': '17496.ro.216.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.ca1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833435
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '108.x1'], 'contains': ['648.l1', '648.bf1', '648.bg1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [112, -1, 7008, -1], 'generators': [12320, 6432, 12528], 'label': '17496.ro.216.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '216.cb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833436
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '108.y1'], 'contains': ['648.m1', '648.bi1', '648.bj1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [1547, -1, 5021, -1], 'generators': [12320, 16224, 8064], 'label': '17496.ro.216.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.cc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cc1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833437
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '108.z1'], 'contains': ['648.n1', '648.o1', '648.r1', '648.u1', '648.x1', '648.ft1', '648.fw1', '648.fz1', '648.gc1', '648.gf1', '648.gi1', '648.gl1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5871, -1, 5410, -1], 'generators': [6488, 3048, 14904, 12312], 'label': '17496.ro.216.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '216.cd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833438
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.f1', '108.ba1'], 'contains': ['648.n1', '648.p1', '648.s1', '648.v1', '648.y1', '648.fu1', '648.fx1', '648.ga1', '648.gd1', '648.gg1', '648.gj1', '648.gm1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3067, -1, 4081, -1], 'generators': [6488, 8232, 7848, 12312], 'label': '17496.ro.216.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.ce1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833439
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '108.bb1'], 'contains': ['648.n1', '648.q1', '648.t1', '648.w1', '648.z1', '648.fv1', '648.fy1', '648.gb1', '648.ge1', '648.gh1', '648.gk1', '648.gn1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4759, -1, 3071, -1], 'generators': [656, 15360, 7200, 12312], 'label': '17496.ro.216.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '216.cf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833440
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.c1'], 'contains': ['72.b1', '72.c1', '72.f1', '72.i1', '72.j1', '72.m1', '72.n1', '72.q1', '72.s1', '72.be1', '72.bg1', '72.bl1', '72.bn1', '72.bs1', '72.bu1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2093, -1, 4314, -1], 'generators': [12320, 15360, 2664, 216], 'label': '17496.ro.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833441
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.i1', '108.bc1'], 'contains': ['648.o1', '648.p1', '648.q1', '648.ba1', '648.bc1', '648.be1', '648.bh1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1677, -1, 7062, -1], 'generators': [6488, 3912, 15624], 'label': '17496.ro.216.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '216.cg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833442
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '108.bd1'], 'contains': ['648.o1', '648.bb1', '648.bd1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2757, -1, 9068, -1], 'generators': [656, 15624, 15120], 'label': '17496.ro.216.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '216.ch1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ch1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833443
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '108.be1'], 'contains': ['648.p1', '648.bf1', '648.bg1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [156, -1, 6953, -1], 'generators': [656, 6432, 12528], 'label': '17496.ro.216.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '216.ci1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ci1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833444
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '108.bf1'], 'contains': ['648.q1', '648.bi1', '648.bj1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1590, -1, 4966, -1], 'generators': [656, 16224, 8064], 'label': '17496.ro.216.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.cj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cj1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833445
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '108.bg1'], 'contains': ['648.bk1', '648.bl1', '648.bs1', '648.bv1', '648.by1', '648.cs1', '648.cv1', '648.cy1', '648.ft1', '648.fw1', '648.fz1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [5658, -1, 6125, -1], 'generators': [12320, 15360, 9792, 5832], 'label': '17496.ro.216.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '216.ck1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ck1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833446
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '108.bh1'], 'contains': ['648.bk1', '648.bm1', '648.bt1', '648.bw1', '648.bz1', '648.ct1', '648.cw1', '648.cz1', '648.fu1', '648.fx1', '648.ga1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [2185, -1, 4104, -1], 'generators': [12320, 9528, 14328, 5832], 'label': '17496.ro.216.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.cl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cl1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833447
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '108.bi1'], 'contains': ['648.bk1', '648.bn1', '648.bu1', '648.bx1', '648.ca1', '648.cu1', '648.cx1', '648.da1', '648.fv1', '648.fy1', '648.gb1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4031, -1, 3264, -1], 'generators': [12320, 3696, 1368, 5832], 'label': '17496.ro.216.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.cm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cm1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833448
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '108.bj1'], 'contains': ['648.bl1', '648.bm1', '648.cb1', '648.ce1', '648.ch1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [1893, -1, 7225, -1], 'generators': [12320, 6720, 13248], 'label': '17496.ro.216.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '216.cn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cn1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833449
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '108.bk1'], 'contains': ['648.bl1', '648.bn1', '648.cc1', '648.cf1', '648.ck1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [2937, -1, 6566, -1], 'generators': [12320, 5208, 7200], 'label': '17496.ro.216.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '216.co1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833451
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.d1'], 'contains': ['72.a1', '72.b1', '72.c1', '72.d1', '72.e1', '72.i1', '72.j1', '72.k1', '72.l1', '72.r1', '72.t1', '72.v1', '72.bc1', '72.bf1', '72.bm1', '72.bo1', '72.bq1', '72.br1', '72.br2'], 'core': '72.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3770, -1, 4808, -1], 'generators': [12320, 15360, 15840, 14904], 'label': '17496.ro.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157833452
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '108.bm1'], 'contains': ['648.bm1', '648.bn1', '648.ci1', '648.cj1', '648.cl1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [1051, -1, 5130, -1], 'generators': [12320, 888, 13032], 'label': '17496.ro.216.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '216.cq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cq1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833453
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '108.bn1'], 'contains': ['648.bo1', '648.bp1', '648.bs1', '648.bv1', '648.by1', '648.fk1', '648.fn1', '648.fq1', '648.gc1', '648.gf1', '648.gi1', '648.gl1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [5807, -1, 5387, -1], 'generators': [11672, 15360, 3240, 5832], 'label': '17496.ro.216.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '216.cr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cr1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833454
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '108.bo1'], 'contains': ['648.bo1', '648.bq1', '648.bt1', '648.bw1', '648.bz1', '648.fl1', '648.fo1', '648.fr1', '648.gd1', '648.gg1', '648.gj1', '648.gm1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3088, -1, 4058, -1], 'generators': [12968, 9528, 14328, 5832], 'label': '17496.ro.216.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '216.cs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833455
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.g1', '108.bp1'], 'contains': ['648.bo1', '648.br1', '648.bu1', '648.bx1', '648.ca1', '648.fm1', '648.fp1', '648.fs1', '648.ge1', '648.gh1', '648.gk1', '648.gn1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [4744, -1, 3094, -1], 'generators': [5840, 3696, 1368, 5832], 'label': '17496.ro.216.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.ct1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ct1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833456
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.j1', '108.bq1'], 'contains': ['648.bp1', '648.bq1', '648.cb1', '648.ce1', '648.ch1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1937, -1, 7171, -1], 'generators': [11672, 11832, 3240], 'label': '17496.ro.216.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '216.cu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cu1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833457
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.k1', '108.br1'], 'contains': ['648.bp1', '648.br1', '648.cc1', '648.cf1', '648.ck1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [2901, -1, 6488, -1], 'generators': [11672, 5208, 7200], 'label': '17496.ro.216.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '216.cv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833458
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '108.bs1'], 'contains': ['648.bp1', '648.cd1', '648.cg1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3961, -1, 8716, -1], 'generators': [11672, 2448, 3240], 'label': '17496.ro.216.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '216.cw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cw1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833459
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '108.bt1'], 'contains': ['648.bq1', '648.br1', '648.ci1', '648.cj1', '648.cl1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1108, -1, 5075, -1], 'generators': [12968, 888, 13032], 'label': '17496.ro.216.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '216.cx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cx1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833460
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.bw1', '72.bw2', '72.bw3'], 'contains': ['648.cm1', '648.co1', '648.cp1', '648.cs1', '648.cy1', '648.dh1', '648.dn1', '648.eg1', '648.fa1', '648.gf1', '648.gl1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [6729, -1, 3002, -1], 'generators': [12320, 3048, 14904, 648], 'label': '17496.ro.216.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.cy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833461
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.bw1', '72.bw3'], 'contains': ['648.cm1', '648.co1', '648.cq1', '648.ct1', '648.cz1', '648.di1', '648.do1', '648.eh1', '648.fb1', '648.gg1', '648.gm1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [3749, -1, 2978, -1], 'generators': [12320, 2400, 2016, 648], 'label': '17496.ro.216.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.cz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cz1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833462
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1', '18.b1', '18.e1', '18.h1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [696, 7220, 8975, 4439], 'generators': [6, 5832, 1368, 9288, 12320, 2472, 6480, 2592, 12], 'label': '17496.ro.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '1944.3559'}
  • id: 157833463
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.e1'], 'contains': ['72.b1', '72.c1', '72.d1', '72.e1', '72.f1', '72.g1', '72.h1', '72.w1', '72.x1', '72.y1', '72.z1', '72.ba1', '72.bb1', '72.bi1', '72.bj1', '72.bw1', '72.bw2', '72.bw3', '72.bx1', '72.by1', '72.by2', '72.by3', '72.bz1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4815, -1, 3168, -1], 'generators': [12320, 5832, 15360, 7200, 10584], 'label': '17496.ro.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833464
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.bw1', '72.bw2'], 'contains': ['648.cm1', '648.co1', '648.cr1', '648.cu1', '648.da1', '648.dj1', '648.dp1', '648.ei1', '648.fc1', '648.gh1', '648.gn1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [6159, -1, 2482, -1], 'generators': [12320, 3696, 7200, 648], 'label': '17496.ro.216.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.da1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.da1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833465
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '72.bw1', '72.bw2', '72.bw3'], 'contains': ['648.cn1', '648.co1', '648.dq1', '648.du1', '648.ej1', '648.ej2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [8993, -1, 79, -1], 'generators': [12320, 14712, 16416], 'label': '17496.ro.216.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.db1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.db1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833466
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.bw1', '72.bx1', '108.bu1'], 'contains': ['648.cn1', '648.cp1', '648.cq1', '648.cr1', '648.dw1', '648.dz1', '648.ff1', '648.fg1', '648.fi1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [9338, -1, 2365, -1], 'generators': [12320, 1320, 17136], 'label': '17496.ro.216.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833467
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.bw3', '72.bx1', '108.bv1'], 'contains': ['648.cn1', '648.cp1', '648.cq1', '648.dx1', '648.ea1', '648.fd1', '648.fh1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [9648, -1, 2684, -1], 'generators': [12320, 14712, 17136], 'label': '17496.ro.216.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833468
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.bw2', '72.bx1', '108.bw1'], 'contains': ['648.cn1', '648.cp1', '648.cr1', '648.dy1', '648.eb1', '648.fe1', '648.fj1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [9374, -1, 2311, -1], 'generators': [12320, 1320, 14904], 'label': '17496.ro.216.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.de1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.de1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833584
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.t1', '108.bh1', '108.by1', '162.n1'], 'contains': ['648.cw1', '972.p1', '972.r1', '972.bm1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [1888, -1, 8049, -1], 'generators': [9300, 12320, 13416, 6696], 'label': '17496.ro.324.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '324.bu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bu1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833469
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.bw1', '72.bx1', '108.bx1'], 'contains': ['648.cm1', '648.cn1', '648.cp1', '648.cs1', '648.cv1', '648.dk1', '648.dr1', '648.ec1', '648.eq1', '648.gc1', '648.gi1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [7521, -1, 3816, -1], 'generators': [12320, 14712, 14904, 648], 'label': '17496.ro.216.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.df1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.df1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833470
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.bw2', '72.bx1', '108.by1'], 'contains': ['648.cm1', '648.cn1', '648.cq1', '648.ct1', '648.cw1', '648.dl1', '648.ds1', '648.ed1', '648.er1', '648.gd1', '648.gj1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [4266, -1, 3025, -1], 'generators': [12320, 14064, 2016, 648], 'label': '17496.ro.216.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833471
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.bw3', '72.bx1', '108.bz1'], 'contains': ['648.cm1', '648.cn1', '648.cr1', '648.cu1', '648.cx1', '648.dm1', '648.dt1', '648.ee1', '648.es1', '648.ge1', '648.gk1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [6344, -1, 2886, -1], 'generators': [12320, 15360, 7200, 648], 'label': '17496.ro.216.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833472
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.bx1', '108.ca1'], 'contains': ['648.cn1', '648.dv1', '648.ef1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9954, -1, 2419, -1], 'generators': [12320, 14712, 10584], 'label': '17496.ro.216.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.di1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.di1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833473
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.bw1', '72.bw2', '72.bw3'], 'contains': ['648.co1', '648.cp1', '648.cq1', '648.cr1', '648.ek1', '648.en1', '648.ev1', '648.ew1', '648.ey1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 192, 'diagramx': [6907, -1, 1331, -1], 'generators': [12320, 3048, 1512], 'label': '17496.ro.216.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dj1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833474
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1'], 'contains': ['72.q1', '72.r1', '72.v1', '72.w1', '72.y1', '72.bb1', '72.bd1', '72.bh1', '72.bl1', '72.bm1', '72.bp1', '72.bq1', '72.bs1', '72.bt1', '72.bv1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3650, -1, 4060, -1], 'generators': [5192, 15360, 7200, 15120], 'label': '17496.ro.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '24.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833475
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.bw1', '72.bw2'], 'contains': ['648.co1', '648.cp1', '648.cq1', '648.el1', '648.eo1', '648.et1', '648.ex1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [6832, -1, 2147, -1], 'generators': [12320, 15768, 14904], 'label': '17496.ro.216.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dk1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833476
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.bw1', '72.bw3'], 'contains': ['648.co1', '648.cp1', '648.cr1', '648.em1', '648.ep1', '648.eu1', '648.ez1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [7252, -1, 1276, -1], 'generators': [12320, 16008, 14472], 'label': '17496.ro.216.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dl1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833477
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.e1', '72.by1', '72.by2', '72.by3'], 'contains': ['648.db1', '648.dd1', '648.de1', '648.dh1', '648.dk1', '648.dn1', '648.eg1', '648.eq1', '648.fa1', '648.fk1', '648.fq1', '648.ft1', '648.fz1', '648.gc1', '648.gl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7078, -1, 3140, -1], 'generators': [6488, 3048, 14904, 648], 'label': '17496.ro.216.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833478
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.f1', '72.by1', '72.by3'], 'contains': ['648.db1', '648.dd1', '648.df1', '648.di1', '648.dl1', '648.do1', '648.eh1', '648.er1', '648.fb1', '648.fl1', '648.fr1', '648.fu1', '648.ga1', '648.gd1', '648.gm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3796, -1, 2955, -1], 'generators': [6488, 2400, 2016, 648], 'label': '17496.ro.216.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dn1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833479
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.g1', '72.by1', '72.by2'], 'contains': ['648.db1', '648.dd1', '648.dg1', '648.dj1', '648.dm1', '648.dp1', '648.ei1', '648.es1', '648.fc1', '648.fm1', '648.fs1', '648.fv1', '648.gb1', '648.ge1', '648.gn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6174, -1, 2458, -1], 'generators': [6488, 1752, 17064, 648], 'label': '17496.ro.216.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.do1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.do1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833480
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.h1', '72.by1', '72.by2', '72.by3'], 'contains': ['648.dc1', '648.dd1', '648.dq1', '648.du1', '648.dv1', '648.ej1', '648.ej2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9108, -1, 25, -1], 'generators': [6488, 14712, 16416], 'label': '17496.ro.216.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.dp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dp1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833481
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.b1', '72.by1', '72.bz1', '108.cb1'], 'contains': ['648.dc1', '648.de1', '648.df1', '648.dg1', '648.dw1', '648.dz1', '648.ev1', '648.ew1', '648.ey1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7114, -1, 2575, -1], 'generators': [6488, 1320, 17136], 'label': '17496.ro.216.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833482
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.by3', '72.bz1', '108.cc1'], 'contains': ['648.dc1', '648.de1', '648.df1', '648.dx1', '648.ea1', '648.et1', '648.ex1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7984, -1, 2738, -1], 'generators': [6488, 14712, 17136], 'label': '17496.ro.216.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dr1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833483
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.by2', '72.bz1', '108.cd1'], 'contains': ['648.dc1', '648.de1', '648.dg1', '648.dy1', '648.eb1', '648.eu1', '648.ez1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8402, -1, 2629, -1], 'generators': [656, 1320, 14904], 'label': '17496.ro.216.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.ds1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ds1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833484
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.e1', '72.by1', '72.bz1', '108.ce1'], 'contains': ['648.db1', '648.dc1', '648.de1', '648.dh1', '648.dr1', '648.ec1', '648.fa1', '648.fk1', '648.fn1', '648.ft1', '648.fw1', '648.gf1', '648.gi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6375, -1, 4368, -1], 'generators': [6488, 14712, 14904, 648], 'label': '17496.ro.216.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833485
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1'], 'contains': ['72.p1', '72.r1', '72.t1', '72.w1', '72.x1', '72.ba1', '72.be1', '72.bg1', '72.bk1', '72.bm1', '72.bn1', '72.bo1', '72.bs1', '72.bt1', '72.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3586, -1, 4200, -1], 'generators': [7784, 10824, 7200, 10584], 'label': '17496.ro.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '24.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833486
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.f1', '72.by2', '72.bz1', '108.cf1'], 'contains': ['648.db1', '648.dc1', '648.df1', '648.di1', '648.ds1', '648.ed1', '648.fb1', '648.fl1', '648.fo1', '648.fu1', '648.fx1', '648.gg1', '648.gj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3764, -1, 3163, -1], 'generators': [6488, 14064, 2016, 648], 'label': '17496.ro.216.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.du1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.du1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833487
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.g1', '72.by3', '72.bz1', '108.cg1'], 'contains': ['648.db1', '648.dc1', '648.dg1', '648.dj1', '648.dt1', '648.ee1', '648.fc1', '648.fm1', '648.fp1', '648.fv1', '648.fy1', '648.gh1', '648.gk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5676, -1, 2909, -1], 'generators': [6488, 1752, 11232, 648], 'label': '17496.ro.216.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.dv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833488
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.bz1', '108.ch1'], 'contains': ['648.dc1', '648.du1', '648.ef1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9446, -1, 2520, -1], 'generators': [656, 14712, 10584], 'label': '17496.ro.216.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.dw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dw1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833489
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.b1', '72.by1', '72.by2', '72.by3'], 'contains': ['648.dd1', '648.de1', '648.df1', '648.dg1', '648.ek1', '648.en1', '648.ev1', '648.ew1', '648.ey1', '648.ff1', '648.fg1', '648.fi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [7637, -1, 950, -1], 'generators': [656, 3048, 1512], 'label': '17496.ro.216.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dx1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833490
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.by1', '72.by2'], 'contains': ['648.dd1', '648.de1', '648.df1', '648.el1', '648.eo1', '648.et1', '648.ex1', '648.fd1', '648.fh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7673, -1, 2093, -1], 'generators': [656, 15768, 14904], 'label': '17496.ro.216.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dy1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833491
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.by1', '72.by3'], 'contains': ['648.dd1', '648.de1', '648.dg1', '648.em1', '648.ep1', '648.eu1', '648.ez1', '648.fe1', '648.fj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7948, -1, 1004, -1], 'generators': [6488, 16008, 14472], 'label': '17496.ro.216.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.dz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dz1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833492
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.z1', '72.bw1', '72.by2', '72.by3'], 'contains': ['648.di1', '648.dj1', '648.dk1', '648.dn1', '648.ej1', '648.en1', '648.et1', '648.eu1', '648.ff1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8509, -1, 1168, -1], 'generators': [16856, 12120, 15120], 'label': '17496.ro.216.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ea1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833493
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ea2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.z1', '72.bw2', '72.by1', '72.by3'], 'contains': ['648.dh1', '648.dj1', '648.dl1', '648.dn1', '648.ej2', '648.en1', '648.et1', '648.ev1', '648.fe1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7753, -1, 841, -1], 'generators': [11024, 12120, 15120], 'label': '17496.ro.216.ea2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ea2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833494
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ea3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.z1', '72.bw3', '72.by1', '72.by2'], 'contains': ['648.dh1', '648.di1', '648.dm1', '648.dn1', '648.ej2', '648.en1', '648.eu1', '648.ev1', '648.fd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7839, -1, 895, -1], 'generators': [5192, 12120, 15120], 'label': '17496.ro.216.ea3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ea3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833495
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.ba1', '72.bw1', '72.by1', '72.by3'], 'contains': ['648.dh1', '648.dj1', '648.dk1', '648.do1', '648.ej2', '648.ep1', '648.ew1', '648.ex1', '648.fg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8074, -1, 1113, -1], 'generators': [16856, 12120, 216], 'label': '17496.ro.216.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eb1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833496
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1'], 'contains': ['72.p1', '72.q1', '72.s1', '72.t1', '72.u1', '72.v1', '72.w1', '72.x1', '72.y1', '72.z1', '72.bc1', '72.bf1', '72.bk1', '72.bl1', '72.bm1', '72.bn1', '72.bo1', '72.bp1', '72.bq1', '72.br1', '72.br2'], 'core': '216.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3897, -1, 4238, -1], 'generators': [5192, 10824, 15624, 10584], 'label': '17496.ro.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '24.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833497
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.ba1', '72.bw3', '72.by1'], 'contains': ['648.dh1', '648.dm1', '648.do1', '648.ej1', '648.ep1', '648.ew1', '648.fh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7911, -1, 787, -1], 'generators': [5192, 12120, 216], 'label': '17496.ro.216.eb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eb2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eb2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833498
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.bb1', '72.bw1', '72.by1', '72.by2'], 'contains': ['648.dh1', '648.di1', '648.dk1', '648.dp1', '648.ej2', '648.eo1', '648.ey1', '648.ez1', '648.fi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7496, -1, 678, -1], 'generators': [11024, 456, 4752], 'label': '17496.ro.216.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ec1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ec1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833499
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ec2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.bb1', '72.bw2', '72.by1'], 'contains': ['648.dh1', '648.dl1', '648.dp1', '648.ej1', '648.eo1', '648.ey1', '648.fj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7209, -1, 460, -1], 'generators': [16856, 456, 4752], 'label': '17496.ro.216.ec2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ec2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ec2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833500
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.bi1', '72.bw1', '72.by1'], 'contains': ['648.dq1', '648.dr1', '648.dz1', '648.eg1', '648.eh1', '648.ei1', '648.en1', '648.eo1', '648.ep1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7459, -1, 134, -1], 'generators': [5192, 9528, 4752], 'label': '17496.ro.216.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ed1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833501
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ed2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.bi1', '72.bw2', '72.by2'], 'contains': ['648.dq1', '648.ds1', '648.eb1', '648.eg1', '648.ei1', '648.en1', '648.eo1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7298, -1, 188, -1], 'generators': [5192, 3696, 4752], 'label': '17496.ro.216.ed2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ed2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833502
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ed3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.bi1', '72.bw3', '72.by3'], 'contains': ['648.dq1', '648.dt1', '648.ea1', '648.eg1', '648.eh1', '648.en1', '648.ep1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7875, -1, 297, -1], 'generators': [5192, 9528, 10584], 'label': '17496.ro.216.ed3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ed3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833503
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.w1', '72.bx1', '72.by1'], 'contains': ['648.dr1', '648.dv1', '648.dw1', '648.dz1', '648.eq1', '648.er1', '648.es1', '648.fd1', '648.fe1', '648.fg1', '648.fh1', '648.fi1', '648.fj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9843, -1, 1766, -1], 'generators': [5192, 10824, 216], 'label': '17496.ro.216.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ee1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ee1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833504
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.x1', '72.bx1', '72.by3'], 'contains': ['648.dt1', '648.dv1', '648.dx1', '648.ea1', '648.eq1', '648.er1', '648.fe1', '648.ff1', '648.fg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9567, -1, 1875, -1], 'generators': [5192, 10824, 10584], 'label': '17496.ro.216.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ef1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ef1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833505
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.y1', '72.bx1', '72.by2'], 'contains': ['648.ds1', '648.dv1', '648.dy1', '648.eb1', '648.eq1', '648.es1', '648.fd1', '648.ff1', '648.fi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9530, -1, 1440, -1], 'generators': [5192, 10824, 15120], 'label': '17496.ro.216.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eg1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833506
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.w1', '72.bw1', '72.by1', '72.bz1'], 'contains': ['648.dr1', '648.du1', '648.dw1', '648.dz1', '648.et1', '648.eu1', '648.ew1', '648.ex1', '648.ey1', '648.ez1', '648.fa1', '648.fb1', '648.fc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8921, -1, 1657, -1], 'generators': [16856, 10824, 216], 'label': '17496.ro.216.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eh1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833507
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1'], 'contains': ['72.p1', '72.q1', '72.r1', '72.s1', '72.t1', '72.u1', '72.v1', '72.z1', '72.ba1', '72.bb1', '72.bc1', '72.bg1', '72.bh1', '72.bi1', '72.bj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4068, -1, 3993, -1], 'generators': [7280, 15360, 10584, 14904], 'label': '17496.ro.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '24.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157833508
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.x1', '72.bw3', '72.by3', '72.bz1'], 'contains': ['648.dt1', '648.du1', '648.dx1', '648.ea1', '648.eu1', '648.ev1', '648.ew1', '648.fa1', '648.fb1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8957, -1, 1821, -1], 'generators': [16856, 10824, 10584], 'label': '17496.ro.216.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ei1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ei1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833509
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.y1', '72.bw2', '72.by2', '72.bz1'], 'contains': ['648.ds1', '648.du1', '648.dy1', '648.eb1', '648.et1', '648.ev1', '648.ey1', '648.fa1', '648.fc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8736, -1, 1059, -1], 'generators': [16856, 10824, 15120], 'label': '17496.ro.216.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ej1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ej1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833510
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.z1', '72.bw1', '72.by1', '72.bz1'], 'contains': ['648.dh1', '648.di1', '648.dj1', '648.du1', '648.dz1', '648.ec1', '648.et1', '648.eu1', '648.ev1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8473, -1, 1712, -1], 'generators': [16856, 456, 15120], 'label': '17496.ro.216.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ek1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ek1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833511
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.ba1', '72.bw2', '72.by2', '72.bz1'], 'contains': ['648.dh1', '648.dj1', '648.du1', '648.eb1', '648.ed1', '648.ew1', '648.ex1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8117, -1, 1385, -1], 'generators': [16856, 456, 216], 'label': '17496.ro.216.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.el1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.el1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833512
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.bb1', '72.bw3', '72.by3', '72.bz1'], 'contains': ['648.dh1', '648.di1', '648.du1', '648.ea1', '648.ee1', '648.ey1', '648.ez1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7790, -1, 1222, -1], 'generators': [16856, 456, 10584], 'label': '17496.ro.216.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.em1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.em1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833513
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.z1', '72.bx1', '72.by1'], 'contains': ['648.dk1', '648.dl1', '648.dm1', '648.dv1', '648.dz1', '648.ec1', '648.fd1', '648.fe1', '648.ff1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9410, -1, 2039, -1], 'generators': [5192, 456, 15120], 'label': '17496.ro.216.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.en1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.en1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833514
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ba1', '72.bx1', '72.by2'], 'contains': ['648.dk1', '648.dm1', '648.dv1', '648.eb1', '648.ed1', '648.fg1', '648.fh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9879, -1, 2202, -1], 'generators': [5192, 456, 216], 'label': '17496.ro.216.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eo1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833515
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bb1', '72.bx1', '72.by3'], 'contains': ['648.dk1', '648.dl1', '648.dv1', '648.ea1', '648.ee1', '648.fi1', '648.fj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9609, -1, 1494, -1], 'generators': [5192, 456, 10584], 'label': '17496.ro.216.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ep1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ep1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833516
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.bj1', '72.bw1', '72.by1'], 'contains': ['648.dn1', '648.do1', '648.dp1', '648.dq1', '648.dw1', '648.ec1', '648.ek1', '648.el1', '648.em1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6401, -1, 1930, -1], 'generators': [3048, 15768, 14904], 'label': '17496.ro.216.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833517
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bj1', '72.bw2', '72.by2'], 'contains': ['648.dn1', '648.dp1', '648.dq1', '648.dy1', '648.ed1', '648.ek1', '648.el1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6437, -1, 1549, -1], 'generators': [8880, 15768, 14904], 'label': '17496.ro.216.eq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eq2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833518
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '9.a1'], 'contains': ['54.d1', '54.e1', '54.f1', '81.b1', '243.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [940, -1, 9870, -1], 'generators': [3469, 5832, 13608, 7206, 12312, 9300, 744], 'label': '17496.ro.27.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833519
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eq3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bj1', '72.bw3', '72.by3'], 'contains': ['648.dn1', '648.do1', '648.dq1', '648.dx1', '648.ee1', '648.ek1', '648.em1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6473, -1, 1984, -1], 'generators': [3048, 9936, 14904], 'label': '17496.ro.216.eq3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eq3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833520
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bi1', '72.bx1', '72.bz1'], 'contains': ['648.dr1', '648.ds1', '648.dt1', '648.dz1', '648.ea1', '648.eb1', '648.ef1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9694, -1, 2256, -1], 'generators': [5192, 15360, 10584], 'label': '17496.ro.216.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.er1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.er1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833521
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bj1', '72.bx1', '72.bz1', '108.ci1'], 'contains': ['648.dw1', '648.dx1', '648.dy1', '648.ec1', '648.ed1', '648.ee1', '648.ef1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8546, -1, 2847, -1], 'generators': [14712, 9936, 14904], 'label': '17496.ro.216.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '216.es1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.es1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833522
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.w1', '72.bw1', '72.by2', '72.by3'], 'contains': ['648.eg1', '648.ej1', '648.ek1', '648.en1', '648.eq1', '648.et1', '648.eu1', '648.ex1', '648.ez1', '648.fb1', '648.fc1', '648.fg1', '648.fi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [9072, -1, 732, -1], 'generators': [11024, 4992, 216], 'label': '17496.ro.216.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.et1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833523
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.et2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.w1', '72.bw2', '72.by1', '72.by3'], 'contains': ['648.eg1', '648.ej2', '648.ek1', '648.en1', '648.er1', '648.et1', '648.ew1', '648.ex1', '648.ey1', '648.fa1', '648.fc1', '648.fe1', '648.fj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8223, -1, 569, -1], 'generators': [16856, 4992, 216], 'label': '17496.ro.216.et2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.et2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833524
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.et3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.w1', '72.bw3', '72.by1', '72.by2'], 'contains': ['648.eg1', '648.ej2', '648.ek1', '648.en1', '648.es1', '648.eu1', '648.ew1', '648.ey1', '648.ez1', '648.fa1', '648.fb1', '648.fd1', '648.fh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8365, -1, 623, -1], 'generators': [5192, 4992, 216], 'label': '17496.ro.216.et3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.et3', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833525
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.x1', '72.bw1', '72.by1', '72.by2'], 'contains': ['648.ei1', '648.ej2', '648.el1', '648.eo1', '648.eq1', '648.eu1', '648.ev1', '648.ew1', '648.fa1', '648.fb1', '648.ff1', '648.fg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8276, -1, 515, -1], 'generators': [16856, 10824, 4752], 'label': '17496.ro.216.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eu1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833526
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.eu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.x1', '72.bw2', '72.by1'], 'contains': ['648.ei1', '648.ej1', '648.el1', '648.eo1', '648.er1', '648.ev1', '648.ew1', '648.fa1', '648.fe1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7349, -1, 351, -1], 'generators': [11024, 10824, 4752], 'label': '17496.ro.216.eu2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.eu2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eu2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833527
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['72.y1', '72.bw1', '72.by1', '72.by3'], 'contains': ['648.eh1', '648.ej2', '648.em1', '648.ep1', '648.eq1', '648.et1', '648.ev1', '648.ey1', '648.fa1', '648.fc1', '648.ff1', '648.fi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8329, -1, 406, -1], 'generators': [16856, 4992, 15120], 'label': '17496.ro.216.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ev1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ev1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833528
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '216.ev2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.y1', '72.bw3', '72.by1'], 'contains': ['648.eh1', '648.ej1', '648.em1', '648.ep1', '648.es1', '648.ev1', '648.ey1', '648.fa1', '648.fd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7600, -1, 242, -1], 'generators': [5192, 4992, 15120], 'label': '17496.ro.216.ev2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '216.ev2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ev2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833529
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.a1'], 'contains': ['54.l1', '54.m1', '54.n1', '81.b1', '243.b1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [1046, -1, 9709, -1], 'generators': [3469, 13608, 744, 7206, 12312, 9300, 12320], 'label': '17496.ro.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833530
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '81.a1'], 'contains': ['486.a1', '486.b1', '486.c1', '729.a1', '729.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [109, -1, 9924, -1], 'generators': [3469, 5832, 4914, 648, 9300], 'label': '17496.ro.243.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833531
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1', '81.a1'], 'contains': ['486.d1', '486.e1', '486.f1', '729.a1', '729.c1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [254, -1, 9647, -1], 'generators': [3469, 12320, 4914, 12312, 9300], 'label': '17496.ro.243.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '243.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833532
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '243.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1'], 'contains': ['486.h1', '486.i1', '486.j1', '729.b1', '729.c1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [294, -1, 9586, -1], 'generators': [3469, 5832, 4914, 9300, 12320], 'label': '17496.ro.243.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '243.c1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157833533
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '162.a1', '162.b1', '162.c1'], 'contains': ['648.a1', '972.a1', '972.b1', '972.c1', '972.d1', '972.e1', '972.f1', '972.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1093, -1, 8820, -1], 'generators': [9300, 12320, 648, 5832], 'label': '17496.ro.324.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833534
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.e1', '108.f1', '108.g1', '108.h1', '108.i1', '108.j1', '108.k1'], 'contains': ['648.b1', '972.a1', '972.h1', '972.l1', '972.t1', '972.u1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4982, -1, 7319, -1], 'generators': [9300, 648, 5832, 14712], 'label': '17496.ro.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833535
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.b1', '108.e1', '108.f1', '108.g1', '108.h1', '108.l1', '108.m1', '108.n1', '108.o1', '108.o2'], 'contains': ['648.d1', '972.a1', '972.i1', '972.m1', '972.v1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2383, -1, 8560, -1], 'generators': [9300, 648, 5832, 5928], 'label': '17496.ro.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833536
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '108.e1', '108.f1', '108.i1', '108.l1', '108.m1', '108.p1', '108.q1'], 'contains': ['648.e1', '972.a1', '972.j1', '972.n1', '972.w1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [590, -1, 8186, -1], 'generators': [9300, 648, 5832, 6720], 'label': '17496.ro.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833537
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.d1', '108.e1', '108.g1', '108.j1', '108.l1', '108.n1', '108.p1', '108.r1'], 'contains': ['648.f1', '972.a1', '972.k1', '972.o1', '972.x1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1415, -1, 6438, -1], 'generators': [9300, 648, 5832, 5208], 'label': '17496.ro.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833538
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.s1', '108.t1', '108.u1'], 'contains': ['648.j1', '972.b1', '972.h1', '972.p1', '972.y1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [2917, -1, 7676, -1], 'generators': [9300, 12320, 12312, 14712], 'label': '17496.ro.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833539
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.b1', '108.s1', '108.v1', '108.w1'], 'contains': ['648.k1', '972.b1', '972.i1', '972.q1', '972.z1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 432, 'diagramx': [2234, -1, 8952, -1], 'generators': [9300, 12320, 12312, 5928], 'label': '17496.ro.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833540
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.b1', '12.c1', '12.d1', '12.e1'], 'contains': ['72.b1', '108.a1', '108.b1', '108.c1', '108.d1', '108.e1', '108.bu1', '108.cb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3993, -1, 6742, -1], 'generators': [9300, 648, 6696, 12320, 5832, 14712], 'label': '17496.ro.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '36.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833541
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '108.t1', '108.v1', '108.x1'], 'contains': ['648.l1', '972.b1', '972.j1', '972.r1', '972.ba1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [684, -1, 8505, -1], 'generators': [9300, 12320, 12312, 11832], 'label': '17496.ro.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833542
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.d1', '108.u1', '108.v1', '108.y1'], 'contains': ['648.m1', '972.b1', '972.k1', '972.s1', '972.bb1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [1329, -1, 6000, -1], 'generators': [9300, 12320, 12312, 7200], 'label': '17496.ro.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833543
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.z1', '108.ba1', '108.bb1'], 'contains': ['648.n1', '972.c1', '972.h1', '972.bc1', '972.bg1', '972.bh1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3697, -1, 7544, -1], 'generators': [9300, 6488, 12312, 14712], 'label': '17496.ro.324.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833544
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.b1', '108.z1', '108.bc1', '108.bd1'], 'contains': ['648.o1', '972.c1', '972.i1', '972.bd1', '972.bi1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [2557, -1, 8864, -1], 'generators': [9300, 6488, 12312, 5568], 'label': '17496.ro.324.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833545
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.c1', '108.ba1', '108.bc1', '108.be1'], 'contains': ['648.p1', '972.c1', '972.j1', '972.be1', '972.bj1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [641, -1, 8352, -1], 'generators': [9300, 6488, 12312, 11832], 'label': '17496.ro.324.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833546
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.d1', '108.bb1', '108.bc1', '108.bf1'], 'contains': ['648.q1', '972.c1', '972.k1', '972.bf1', '972.bk1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1674, -1, 5790, -1], 'generators': [9300, 6488, 12312, 7200], 'label': '17496.ro.324.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833547
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.bg1', '108.bh1', '108.bi1'], 'contains': ['648.bk1', '972.d1', '972.l1', '972.p1', '972.bc1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [3011, -1, 7632, -1], 'generators': [9300, 12320, 5832, 14712], 'label': '17496.ro.324.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833548
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.b1', '108.bg1', '108.bj1', '108.bk1', '108.bl1'], 'contains': ['648.bl1', '972.d1', '972.m1', '972.q1', '972.bd1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 432, 'diagramx': [2506, -1, 8908, -1], 'generators': [9300, 12320, 5832, 5568], 'label': '17496.ro.324.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.o1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833549
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '108.bh1', '108.bj1', '108.bm1'], 'contains': ['648.bm1', '972.d1', '972.n1', '972.r1', '972.be1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [778, -1, 8276, -1], 'generators': [9300, 12320, 5832, 11832], 'label': '17496.ro.324.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.p1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833550
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.d1', '108.bi1', '108.bk1', '108.bm1'], 'contains': ['648.bn1', '972.d1', '972.o1', '972.s1', '972.bf1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [1544, -1, 6091, -1], 'generators': [9300, 12320, 5832, 7200], 'label': '17496.ro.324.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.q1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833551
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.d1', '12.e1'], 'contains': ['72.c1', '108.a1', '108.b1', '108.c1', '108.f1', '108.bv1', '108.cc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4315, -1, 7133, -1], 'generators': [9300, 648, 3240, 12320, 5832, 9936], 'label': '17496.ro.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '36.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833552
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.bn1', '108.bo1', '108.bp1'], 'contains': ['648.bo1', '972.e1', '972.l1', '972.y1', '972.bg1', '972.bh1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 432, 'diagramx': [3647, -1, 7363, -1], 'generators': [9300, 11672, 5832, 14712], 'label': '17496.ro.324.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.r1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833553
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.b1', '108.bn1', '108.bq1', '108.br1', '108.bs1'], 'contains': ['648.bp1', '972.e1', '972.m1', '972.z1', '972.bi1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 864, 'diagramx': [2421, -1, 8635, -1], 'generators': [9300, 11672, 5832, 15864], 'label': '17496.ro.324.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.s1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833554
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.c1', '108.bo1', '108.bq1', '108.bt1'], 'contains': ['648.bq1', '972.e1', '972.n1', '972.ba1', '972.bj1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 432, 'diagramx': [928, -1, 8142, -1], 'generators': [9300, 11672, 5832, 11832], 'label': '17496.ro.324.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.t1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833555
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.d1', '108.bp1', '108.br1', '108.bt1'], 'contains': ['648.br1', '972.e1', '972.o1', '972.bb1', '972.bk1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 432, 'diagramx': [1587, -1, 5956, -1], 'generators': [9300, 11672, 5832, 7200], 'label': '17496.ro.324.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.u1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833556
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.bx1', '108.by1', '108.bz1'], 'contains': ['648.cm1', '972.f1', '972.p1', '972.t1', '972.bg1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [4636, -1, 6753, -1], 'generators': [9300, 12320, 6480, 14712], 'label': '17496.ro.324.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.v1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833557
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.bu1', '108.bv1', '108.bw1', '108.bx1', '108.by1', '108.bz1', '108.ca1'], 'contains': ['648.cn1', '972.f1', '972.p1', '972.u1', '972.bh1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [4731, -1, 5834, -1], 'generators': [9300, 12320, 648, 14712], 'label': '17496.ro.324.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.w1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833558
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.b1', '108.bu1', '108.bv1', '108.bw1', '108.bx1'], 'contains': ['648.cp1', '972.f1', '972.q1', '972.v1', '972.bi1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 864, 'diagramx': [4702, -1, 6709, -1], 'generators': [9300, 12320, 648, 5568], 'label': '17496.ro.324.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.x1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833559
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.c1', '108.bu1', '108.bv1', '108.by1'], 'contains': ['648.cq1', '972.f1', '972.r1', '972.w1', '972.bj1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 432, 'diagramx': [3511, -1, 6841, -1], 'generators': [9300, 12320, 6480, 11832], 'label': '17496.ro.324.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.y1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833560
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.d1', '108.bu1', '108.bw1', '108.bz1'], 'contains': ['648.cr1', '972.f1', '972.s1', '972.x1', '972.bk1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 432, 'diagramx': [4760, -1, 5475, -1], 'generators': [9300, 12320, 6480, 7200], 'label': '17496.ro.324.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.z1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833561
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.ce1', '108.cf1', '108.cg1'], 'contains': ['648.db1', '972.g1', '972.t1', '972.y1', '972.bc1', '972.bh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4456, -1, 7275, -1], 'generators': [9300, 6488, 6480, 14712], 'label': '17496.ro.324.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.ba1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833562
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.d1', '12.e1'], 'contains': ['72.d1', '108.a1', '108.b1', '108.d1', '108.g1', '108.bw1', '108.cd1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4354, -1, 6494, -1], 'generators': [9300, 648, 16704, 12320, 5832, 14712], 'label': '17496.ro.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '36.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833563
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.cb1', '108.cc1', '108.cd1', '108.ce1', '108.cf1', '108.cg1', '108.ch1'], 'contains': ['648.dc1', '972.g1', '972.u1', '972.y1', '972.bc1', '972.bg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4672, -1, 6797, -1], 'generators': [9300, 6488, 648, 14712], 'label': '17496.ro.324.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.bb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833564
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['108.b1', '108.cb1', '108.cc1', '108.cd1', '108.ce1'], 'contains': ['648.de1', '972.g1', '972.v1', '972.z1', '972.bd1', '972.bi1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': [4607, -1, 7588, -1], 'generators': [9300, 6488, 648, 5568], 'label': '17496.ro.324.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.bc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833565
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.c1', '108.cb1', '108.cc1', '108.cf1'], 'contains': ['648.df1', '972.g1', '972.w1', '972.ba1', '972.be1', '972.bj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1271, -1, 7453, -1], 'generators': [9300, 6488, 6480, 11832], 'label': '17496.ro.324.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.bd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833566
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.d1', '108.cb1', '108.cd1', '108.cg1'], 'contains': ['648.dg1', '972.g1', '972.x1', '972.bb1', '972.bf1', '972.bk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [4506, -1, 5621, -1], 'generators': [9300, 6488, 648, 7200], 'label': '17496.ro.324.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '324.be1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833567
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.h1', '108.s1', '108.z1'], 'contains': ['648.u1', '972.h1', '972.i1', '972.bl1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3242, -1, 7956, -1], 'generators': [9300, 12312, 14712, 16272], 'label': '17496.ro.324.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bf1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833568
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.i1', '108.t1', '108.ba1', '162.d1'], 'contains': ['648.v1', '972.h1', '972.j1', '972.bm1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1825, -1, 8231, -1], 'generators': [9300, 12312, 16152, 9936], 'label': '17496.ro.324.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '324.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bg1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833569
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.u1', '108.bb1', '162.e1'], 'contains': ['648.w1', '972.h1', '972.k1', '972.bn1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2709, -1, 6393, -1], 'generators': [9300, 12312, 14712, 7200], 'label': '17496.ro.324.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bh1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833570
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.l1', '108.v1', '108.bc1'], 'contains': ['648.bc1', '972.i1', '972.j1', '972.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1153, -1, 8314, -1], 'generators': [9300, 2616, 2880, 12312], 'label': '17496.ro.324.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '324.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bi1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833571
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.o2', '108.w1', '108.bd1', '162.f1', '162.g1', '162.h1'], 'contains': ['648.bd1', '972.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2166, -1, 9703, -1], 'generators': [9300, 2616, 16704, 12312], 'label': '17496.ro.324.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bj1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833572
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.q1', '108.x1', '108.be1', '162.i1'], 'contains': ['648.bg1', '972.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [11, -1, 8598, -1], 'generators': [1956, 7728, 6696, 12312], 'label': '17496.ro.324.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '324.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bk1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833573
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.c1', '18.a1', '18.f1', '18.i1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [938, 3898, 8871, 2396], 'generators': [4255, 5832, 3312, 4104, 17292, 8232, 648, 9072, 12320], 'label': '17496.ro.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 157833574
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1'], 'contains': ['72.e1', '108.a1', '108.b1', '108.h1', '108.s1', '108.z1', '108.bg1', '108.bn1', '108.bx1', '108.ce1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3515, -1, 7211, -1], 'generators': [9300, 3240, 14712, 12320, 648, 5832], 'label': '17496.ro.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '36.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833575
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.r1', '108.y1', '108.bf1', '162.j1'], 'contains': ['648.bj1', '972.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1132, -1, 5360, -1], 'generators': [8724, 13848, 7200, 12312], 'label': '17496.ro.324.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '324.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bl1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833576
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.h1', '108.bg1', '108.bn1'], 'contains': ['648.bv1', '972.l1', '972.m1', '972.bl1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3273, -1, 7909, -1], 'generators': [9300, 5832, 14712, 16272], 'label': '17496.ro.324.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.bm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bm1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833577
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.i1', '108.bh1', '108.bo1', '162.k1'], 'contains': ['648.bw1', '972.l1', '972.n1', '972.bm1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2022, -1, 8096, -1], 'generators': [9300, 5832, 16152, 9936], 'label': '17496.ro.324.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '324.bn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bn1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833578
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.bi1', '108.bp1', '162.l1'], 'contains': ['648.bx1', '972.l1', '972.o1', '972.bn1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2799, -1, 6346, -1], 'generators': [9300, 5832, 14712, 7200], 'label': '17496.ro.324.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.bo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bo1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833579
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.m1', '108.bj1', '108.bq1'], 'contains': ['648.ce1', '972.m1', '972.n1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1785, -1, 8673, -1], 'generators': [9300, 16080, 6696, 5832], 'label': '17496.ro.324.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '324.bp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833580
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.n1', '108.bk1', '108.br1'], 'contains': ['648.cf1', '972.m1', '972.o1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2201, -1, 6910, -1], 'generators': [9300, 5208, 7200, 5832], 'label': '17496.ro.324.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '324.bq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833581
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.o1', '108.bl1', '108.bs1'], 'contains': ['648.cg1', '972.m1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3331, -1, 8990, -1], 'generators': [9300, 3744, 3240, 5832], 'label': '17496.ro.324.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '324.br1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.br1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833582
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.p1', '108.bm1', '108.bt1', '162.m1'], 'contains': ['648.cj1', '972.n1', '972.o1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [753, -1, 6878, -1], 'generators': [9300, 8664, 2880, 5832], 'label': '17496.ro.324.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '324.bs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bs1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833583
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.s1', '108.bg1', '108.bx1'], 'contains': ['648.cv1', '972.p1', '972.q1', '972.bl1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [3304, -1, 7815, -1], 'generators': [9300, 12320, 14712, 16272], 'label': '17496.ro.324.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.bt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bt1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833585
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.e1', '18.a1'], 'contains': ['72.f1', '108.a1', '108.c1', '108.i1', '108.t1', '108.ba1', '108.bh1', '108.bo1', '108.by1', '108.cf1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2635, -1, 7264, -1], 'generators': [9300, 6696, 13416, 12320, 648, 5832], 'label': '17496.ro.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833586
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.u1', '108.bi1', '108.bz1', '162.o1'], 'contains': ['648.cx1', '972.p1', '972.s1', '972.bn1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [2740, -1, 6046, -1], 'generators': [3900, 12320, 13416, 9936], 'label': '17496.ro.324.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.bv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bv1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833587
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.e1', '108.bu1', '108.cb1', '108.ci1'], 'contains': ['648.dw1', '972.u1', '972.v1', '972.w1', '972.x1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5169, -1, 5659, -1], 'generators': [9300, 16008, 7200, 6480], 'label': '17496.ro.324.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '324.bw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bw1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833588
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.f1', '108.bv1', '108.cc1', '108.ci1'], 'contains': ['648.dx1', '972.u1', '972.v1', '972.w1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5043, -1, 5872, -1], 'generators': [9300, 14712, 16488, 648], 'label': '17496.ro.324.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '324.bx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bx1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833589
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.g1', '108.bw1', '108.cd1', '108.ci1'], 'contains': ['648.dy1', '972.u1', '972.v1', '972.x1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5448, -1, 5437, -1], 'generators': [9300, 14712, 6768, 648], 'label': '17496.ro.324.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '324.by1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.by1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833590
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.h1', '108.bx1', '108.ce1', '108.ci1'], 'contains': ['648.ec1', '972.t1', '972.u1', '972.v1', '972.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5142, -1, 6617, -1], 'generators': [9300, 6480, 14712, 16272], 'label': '17496.ro.324.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.bz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bz1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833591
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.i1', '108.by1', '108.cf1', '108.ci1'], 'contains': ['648.ed1', '972.t1', '972.u1', '972.w1', '972.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3841, -1, 6663, -1], 'generators': [9300, 648, 16152, 9936], 'label': '17496.ro.324.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '324.ca1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ca1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833592
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.bz1', '108.cg1', '108.ci1'], 'contains': ['648.ee1', '972.t1', '972.u1', '972.x1', '972.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5195, -1, 5575, -1], 'generators': [3900, 648, 13416, 9936], 'label': '17496.ro.324.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '324.cb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833593
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1', '108.ca1', '108.ch1', '108.ci1', '162.p1'], 'contains': ['648.ef1', '972.u1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6999, -1, 4030, -1], 'generators': [9300, 14712, 9936, 648], 'label': '17496.ro.324.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '324.cc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cc1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833594
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.s1', '108.bn1', '108.ce1'], 'contains': ['648.fn1', '972.y1', '972.z1', '972.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3357, -1, 7862, -1], 'generators': [9300, 7136, 14712, 16272], 'label': '17496.ro.324.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.cd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833595
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.t1', '108.bo1', '108.cf1'], 'contains': ['648.fo1', '972.y1', '972.ba1', '972.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1948, -1, 7722, -1], 'generators': [9300, 16, 13416, 6696], 'label': '17496.ro.324.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '324.ce1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ce1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833596
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.e1', '18.b1'], 'contains': ['72.g1', '108.a1', '108.d1', '108.j1', '108.u1', '108.bb1', '108.bi1', '108.bp1', '108.bz1', '108.cg1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3662, -1, 6283, -1], 'generators': [9300, 7200, 14712, 12320, 648, 5832], 'label': '17496.ro.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833597
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.u1', '108.bp1', '108.cg1', '162.q1'], 'contains': ['648.fp1', '972.y1', '972.bb1', '972.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2837, -1, 5911, -1], 'generators': [3900, 7136, 13416, 9936], 'label': '17496.ro.324.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.cf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cf1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833598
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.z1', '108.bg1', '108.ce1'], 'contains': ['648.fw1', '972.bc1', '972.bd1', '972.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3459, -1, 7768, -1], 'generators': [9300, 6488, 14712, 16272], 'label': '17496.ro.324.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.cg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833599
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.ba1', '108.bh1', '108.cf1', '162.r1'], 'contains': ['648.fx1', '972.bc1', '972.be1', '972.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1857, -1, 8002, -1], 'generators': [9300, 6488, 13416, 6696], 'label': '17496.ro.324.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '324.ch1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ch1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833600
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bb1', '108.bi1', '108.cg1'], 'contains': ['648.fy1', '972.bc1', '972.bf1', '972.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3062, -1, 5744, -1], 'generators': [3900, 656, 13416, 9936], 'label': '17496.ro.324.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '324.ci1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ci1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833601
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.z1', '108.bn1', '108.bx1', '108.ce1'], 'contains': ['648.gi1', '972.bg1', '972.bh1', '972.bi1', '972.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4395, -1, 7499, -1], 'generators': [9300, 5840, 14712, 16272], 'label': '17496.ro.324.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '324.cj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833602
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.ba1', '108.bo1', '108.by1', '108.cf1'], 'contains': ['648.gj1', '972.bg1', '972.bh1', '972.bj1', '972.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4043, -1, 7408, -1], 'generators': [9300, 5848, 13416, 6696], 'label': '17496.ro.324.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '324.ck1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ck1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833603
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '324.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.bb1', '108.bp1', '108.bz1', '108.cg1'], 'contains': ['648.gk1', '972.bg1', '972.bh1', '972.bk1', '972.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4426, -1, 5698, -1], 'generators': [3900, 11672, 13416, 9936], 'label': '17496.ro.324.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '324.cl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cl1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833604
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.d1', '54.g1', '162.a1', '243.a1'], 'contains': ['972.a1', '1458.a1', '1458.d1', '1458.j1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [464, -1, 9815, -1], 'generators': [3469, 648, 5832, 9300], 'label': '17496.ro.486.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833605
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1', '54.e1', '54.h1', '162.b1', '243.a1'], 'contains': ['972.a1', '1458.b1', '1458.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [59, -1, 9909, -1], 'generators': [6, 648, 12, 5832], 'label': '17496.ro.486.b1', 'mobius_quo': None, 'mobius_sub': 9, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833606
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.f1', '54.i1', '162.c1', '243.a1'], 'contains': ['972.a1', '1458.c1', '1458.f1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [128, -1, 9768, -1], 'generators': [4255, 648, 17292, 5832], 'label': '17496.ro.486.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833607
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.c1'], 'contains': ['72.h1', '108.a1', '108.k1', '108.ca1', '108.ch1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6465, -1, 4590, -1], 'generators': [9300, 648, 9936, 12320, 5832, 14712], 'label': '17496.ro.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833608
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1', '162.a1', '243.b1'], 'contains': ['972.b1', '1458.a1', '1458.g1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [502, -1, 9663, -1], 'generators': [3469, 12312, 9300, 12320], 'label': '17496.ro.486.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833609
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1', '54.m1', '54.o1', '162.b1', '243.b1'], 'contains': ['972.b1', '1458.b1', '1458.h1', '1458.k1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [276, -1, 9617, -1], 'generators': [6, 12312, 12320, 12], 'label': '17496.ro.486.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833610
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1', '54.n1', '54.p1', '162.c1', '243.b1'], 'contains': ['972.b1', '1458.c1', '1458.i1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [314, -1, 9570, -1], 'generators': [4255, 12312, 17292, 12320], 'label': '17496.ro.486.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833611
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.q1', '54.r1', '54.s1', '162.c1'], 'contains': ['972.c1', '1458.c1', '1458.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [433, -1, 9297, -1], 'generators': [4255, 12312, 17292, 656], 'label': '17496.ro.486.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.g1', 'old_label': '486.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833612
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1', '162.a1', '243.c1'], 'contains': ['972.d1', '1458.d1', '1458.g1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [533, -1, 9455, -1], 'generators': [3469, 5832, 9300, 12320], 'label': '17496.ro.486.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.h1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833613
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.u1', '162.b1', '243.c1'], 'contains': ['972.d1', '1458.e1', '1458.h1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [230, -1, 9513, -1], 'generators': [6, 12320, 12, 5832], 'label': '17496.ro.486.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.i1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833614
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1', '162.c1', '243.c1'], 'contains': ['972.d1', '1458.f1', '1458.i1', '1458.l1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [375, -1, 9384, -1], 'generators': [4255, 17292, 12320, 5832], 'label': '17496.ro.486.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.j1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157833615
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.w1', '162.b1'], 'contains': ['972.e1', '1458.e1', '1458.k1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 162, 'diagramx': [402, -1, 9344, -1], 'generators': [6, 12968, 12, 5832], 'label': '17496.ro.486.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1', 'old_label': '486.k1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833616
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1', '162.a1'], 'contains': ['972.f1', '1458.g1', '1458.j1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 162, 'diagramx': [2155, -1, 9173, -1], 'generators': [3469, 648, 9300, 12320], 'label': '17496.ro.486.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '486.l1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833617
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.d1', '162.k1', '162.n1', '162.r1'], 'contains': ['972.bm1', '4374.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [710, -1, 9245, -1], 'generators': [8155, 8100, 10896, 14976], 'label': '17496.ro.486.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.d1', 'old_label': '486.m1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.m1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833618
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.d1'], 'contains': ['72.i1', '108.b1', '108.c1', '108.d1', '108.l1', '108.v1', '108.bc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1734, -1, 7632, -1], 'generators': [9300, 12312, 16272, 12320, 5832, 5208], 'label': '17496.ro.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '36.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833619
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '486.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.e1', '162.l1', '162.o1', '162.q1'], 'contains': ['972.bn1', '4374.b1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [960, -1, 9023, -1], 'generators': [6, 12, 8016, 10584], 'label': '17496.ro.486.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '486.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.n1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833620
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.c1', '216.d1', '216.e1', '324.a1'], 'contains': ['1944.a1', '1944.b1', '1944.c1', '1944.d1', '1944.m1', '1944.v1', '1944.bb1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2257, 7450, 4822, 8848], 'generators': [12320, 648, 5832], 'label': '17496.ro.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['72.a1'], 'normal_contains': ['1944.a1', '1944.b1', '1944.c1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': None, 'quotient_action_image': '4.2', 'quotient_action_kernel': '162.54', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833621
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.f1', '216.g1', '216.h1', '216.i1', '216.j1', '216.k1', '216.l1', '216.m1', '216.n1', '216.o1', '216.p1', '216.q1', '216.r1', '216.s1', '324.b1'], 'contains': ['1944.a1', '1944.e1', '1944.n1', '1944.bc1', '1944.bd1', '1944.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5255, -1, 3616, -1], 'generators': [10584, 648, 5832], 'label': '17496.ro.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833622
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.f1', '216.g1', '216.h1', '216.i1', '216.t1', '216.u1', '216.v1', '216.w1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.bb1', '216.bc1'], 'contains': ['1944.a1', '1944.f1', '1944.o1', '1944.bf1', '1944.bg1', '1944.bh1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5998, -1, 3546, -1], 'generators': [5456, 648, 5832], 'label': '17496.ro.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833623
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.c1', '216.j1', '216.k1', '216.l1', '216.p1', '216.t1', '216.u1', '216.v1', '216.ba1', '216.bd1', '216.be1', '216.bf1', '216.bg1', '216.bg2', '216.bh1', '216.bi1', '216.bj1', '216.bk1', '324.c1'], 'contains': ['1944.a1', '1944.g1', '1944.p1', '1944.bi1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2930, -1, 5533, -1], 'generators': [7224, 648, 5832], 'label': '17496.ro.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833624
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.d1', '216.j1', '216.k1', '216.q1', '216.w1', '216.x1', '216.bb1', '216.bh1', '216.bi1', '216.bl1', '216.bm1', '216.bn1', '216.bo1', '216.bp1', '216.bq1', '324.d1'], 'contains': ['1944.a1', '1944.h1', '1944.q1', '1944.bj1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [845, -1, 4688, -1], 'generators': [11832, 648, 5832], 'label': '17496.ro.648.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833644
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '216.by1', '216.cf1', '324.bh1'], 'contains': ['1944.e1', '1944.i1', '1944.ch1', '1944.cq1', '1944.cz1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3384, -1, 3662, -1], 'generators': [12768, 15768, 12312], 'label': '17496.ro.648.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.w1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833625
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '216.j1', '216.l1', '216.r1', '216.y1', '216.z1', '216.bc1', '216.bh1', '216.bj1', '216.bp1', '216.br1', '216.bs1', '216.bt1', '216.bu1', '216.bv1', '324.e1'], 'contains': ['1944.a1', '1944.i1', '1944.r1', '1944.bk1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1725, -1, 4284, -1], 'generators': [11040, 648, 5832], 'label': '17496.ro.648.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833626
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.f1', '216.m1', '216.n1', '216.o1', '216.t1', '216.u1', '216.w1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.bd1', '216.be1', '216.bf1', '216.bg1', '216.bg2', '216.bl1', '216.bm1', '216.br1', '216.bs1'], 'contains': ['1944.a1', '1944.j1', '1944.s1', '1944.bl1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3480, -1, 4665, -1], 'generators': [6680, 648, 5832], 'label': '17496.ro.648.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833627
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.d1', '216.g1', '216.m1', '216.n1', '216.t1', '216.v1', '216.y1', '216.bb1', '216.bd1', '216.be1', '216.bl1', '216.bn1', '216.bo1', '216.br1', '216.bt1'], 'contains': ['1944.a1', '1944.k1', '1944.t1', '1944.bm1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1474, -1, 4237, -1], 'generators': [776, 648, 5832], 'label': '17496.ro.648.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833628
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '216.h1', '216.m1', '216.o1', '216.u1', '216.v1', '216.w1', '216.bc1', '216.bd1', '216.bf1', '216.bm1', '216.bn1', '216.bs1', '216.bt1', '216.bu1'], 'contains': ['1944.a1', '1944.l1', '1944.u1', '1944.bn1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2683, -1, 4145, -1], 'generators': [7280, 648, 5832], 'label': '17496.ro.648.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833629
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.d1'], 'contains': ['72.j1', '108.b1', '108.c1', '108.m1', '108.bj1', '108.bq1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2237, -1, 8050, -1], 'generators': [9300, 5832, 6768, 12320, 648, 6720], 'label': '17496.ro.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '36.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833630
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.bw1', '216.bx1', '216.by1', '324.f1'], 'contains': ['1944.b1', '1944.e1', '1944.f1', '1944.w1', '1944.x1', '1944.bo1', '1944.bp1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4307, -1, 4168, -1], 'generators': [12320, 15768, 12312], 'label': '17496.ro.648.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833631
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.bw1', '216.bz1', '216.ca1', '324.g1'], 'contains': ['1944.b1', '1944.g1', '1944.j1', '1944.y1', '1944.bq1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [3152, -1, 7363, -1], 'generators': [12320, 15864, 12312], 'label': '17496.ro.648.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '648.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833632
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.d1', '216.bx1', '216.bz1', '216.cb1', '324.h1'], 'contains': ['1944.b1', '1944.h1', '1944.k1', '1944.z1', '1944.br1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [904, -1, 5692, -1], 'generators': [12320, 888, 12312], 'label': '17496.ro.648.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833633
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '216.by1', '216.bz1', '216.cc1', '324.i1'], 'contains': ['1944.b1', '1944.i1', '1944.l1', '1944.ba1', '1944.bs1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1755, -1, 4396, -1], 'generators': [12320, 7200, 12312], 'label': '17496.ro.648.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833634
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '216.cd1', '216.ce1', '216.cf1', '324.j1'], 'contains': ['1944.d1', '1944.e1', '1944.f1', '1944.bt1', '1944.bu1', '1944.by1', '1944.bz1', '1944.ca1', '1944.cb1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5546, -1, 4029, -1], 'generators': [6488, 15768, 12312], 'label': '17496.ro.648.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833635
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.c1', '216.cd1', '216.cg1', '216.ch1', '324.k1'], 'contains': ['1944.d1', '1944.g1', '1944.j1', '1944.bv1', '1944.cc1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3182, -1, 6529, -1], 'generators': [6488, 15864, 12312], 'label': '17496.ro.648.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '648.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833636
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.d1', '216.ce1', '216.cg1', '216.ci1', '324.l1'], 'contains': ['1944.d1', '1944.h1', '1944.k1', '1944.bw1', '1944.cd1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [787, -1, 5487, -1], 'generators': [6488, 888, 12312], 'label': '17496.ro.648.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833637
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '216.cf1', '216.cg1', '216.cj1', '324.m1'], 'contains': ['1944.d1', '1944.i1', '1944.l1', '1944.bx1', '1944.ce1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2127, -1, 4307, -1], 'generators': [6488, 7200, 12312], 'label': '17496.ro.648.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833638
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '216.bw1', '216.cd1'], 'contains': ['1944.e1', '1944.f1', '1944.j1', '1944.ci1', '1944.cl1', '1944.cr1', '1944.cu1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6112, -1, 4483, -1], 'generators': [5192, 456, 12312], 'label': '17496.ro.648.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833639
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '216.bx1', '216.ce1'], 'contains': ['1944.e1', '1944.f1', '1944.k1', '1944.cj1', '1944.cm1', '1944.cs1', '1944.cv1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3654, -1, 3913, -1], 'generators': [9512, 4488, 12312], 'label': '17496.ro.648.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833640
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.d1'], 'contains': ['72.k1', '108.b1', '108.d1', '108.n1', '108.bk1', '108.br1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2466, -1, 6997, -1], 'generators': [9300, 5832, 7200, 12320, 648, 5208], 'label': '17496.ro.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '36.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833641
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.h1', '216.by1', '216.cf1'], 'contains': ['1944.e1', '1944.f1', '1944.l1', '1944.ck1', '1944.cn1', '1944.ct1', '1944.cw1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4880, -1, 3408, -1], 'generators': [9512, 456, 12312], 'label': '17496.ro.648.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833642
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '216.bw1', '216.cd1', '324.bf1'], 'contains': ['1944.e1', '1944.g1', '1944.cf1', '1944.co1', '1944.cx1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5697, -1, 5649, -1], 'generators': [3048, 15624, 12312], 'label': '17496.ro.648.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833643
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.bx1', '216.ce1', '324.bg1'], 'contains': ['1944.e1', '1944.h1', '1944.cg1', '1944.cp1', '1944.cy1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1925, -1, 4260, -1], 'generators': [16800, 10584, 12312], 'label': '17496.ro.648.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '648.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833645
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ba1', '216.bw1', '216.cd1'], 'contains': ['1944.f1', '1944.g1', '1944.j1', '1944.da1', '1944.dd1', '1944.dd2', '1944.dg1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5936, -1, 5820, -1], 'generators': [7784, 10824, 12312], 'label': '17496.ro.648.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833646
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bb1', '216.bx1', '216.ce1'], 'contains': ['1944.f1', '1944.h1', '1944.k1', '1944.db1', '1944.de1', '1944.de2', '1944.dh1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1220, -1, 4052, -1], 'generators': [9512, 12048, 12312], 'label': '17496.ro.648.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833647
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bc1', '216.by1', '216.cf1'], 'contains': ['1944.f1', '1944.i1', '1944.l1', '1944.dc1', '1944.df1', '1944.df2', '1944.di1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3965, -1, 3454, -1], 'generators': [9512, 11040, 12312], 'label': '17496.ro.648.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833648
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.bd1', '216.bz1', '216.cg1'], 'contains': ['1944.g1', '1944.j1', '1944.k1', '1944.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [2184, -1, 5841, -1], 'generators': [15200, 13632], 'label': '17496.ro.648.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '648.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ba1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833649
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bg1', '216.ca1', '216.ch1'], 'contains': ['1944.g1', '1944.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2807, -1, 8245, -1], 'generators': [5192, 7224], 'label': '17496.ro.648.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bb1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833650
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bh1', '216.bz1', '216.cg1', '324.bi1'], 'contains': ['1944.g1', '1944.h1', '1944.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1330, -1, 6444, -1], 'generators': [8448, 7200], 'label': '17496.ro.648.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '648.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833651
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1'], 'contains': ['72.l1', '108.b1', '108.o1', '108.bl1', '108.bs1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3033, -1, 8319, -1], 'generators': [9300, 5832, 3240, 12320, 648, 3744], 'label': '17496.ro.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '36.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833652
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.ca1', '216.ch1', '324.bj1'], 'contains': ['1944.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2452, -1, 9095, -1], 'generators': [13632, 17352], 'label': '17496.ro.648.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bd1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833653
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bm1', '216.bz1', '216.cg1'], 'contains': ['1944.h1', '1944.j1', '1944.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1687, -1, 5778, -1], 'generators': [17432, 13560], 'label': '17496.ro.648.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '648.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.be1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833654
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bo1', '216.cb1', '216.ci1'], 'contains': ['1944.h1', '1944.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [162, -1, 5670, -1], 'generators': [12536, 12048], 'label': '17496.ro.648.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.n1', 'old_label': '648.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bf1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833655
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bq1', '216.cb1', '216.ci1', '324.bk1'], 'contains': ['1944.h1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [25, -1, 6423, -1], 'generators': [6432, 12528], 'label': '17496.ro.648.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '648.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bg1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833656
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.br1', '216.bz1', '216.cg1'], 'contains': ['1944.i1', '1944.j1', '1944.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1352, -1, 5757, -1], 'generators': [8456, 2880], 'label': '17496.ro.648.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '648.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bh1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833657
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bu1', '216.cc1', '216.cj1'], 'contains': ['1944.i1', '1944.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1611, -1, 4328, -1], 'generators': [8672, 7200], 'label': '17496.ro.648.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.o1', 'old_label': '648.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bi1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833658
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bv1', '216.cc1', '216.cj1', '324.bl1'], 'contains': ['1944.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1317, -1, 4438, -1], 'generators': [3480, 7200], 'label': '17496.ro.648.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '648.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bj1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833659
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.ck1', '216.cl1', '216.cm1', '324.n1'], 'contains': ['1944.c1', '1944.n1', '1944.o1', '1944.w1', '1944.x1', '1944.bt1', '1944.bu1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [4470, -1, 4098, -1], 'generators': [12320, 10584, 5832], 'label': '17496.ro.648.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.bk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833660
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.ck1', '216.cn1', '216.co1', '216.cp1', '324.o1'], 'contains': ['1944.c1', '1944.p1', '1944.s1', '1944.y1', '1944.bv1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [4116, -1, 6552, -1], 'generators': [12320, 15864, 5832], 'label': '17496.ro.648.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '648.bl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833661
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.d1', '216.cl1', '216.cn1', '216.cq1', '324.p1'], 'contains': ['1944.c1', '1944.q1', '1944.t1', '1944.z1', '1944.bw1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [989, -1, 4798, -1], 'generators': [12320, 6720, 5832], 'label': '17496.ro.648.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.bm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833662
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '18.d1', '18.e1', '18.f1'], 'contains': ['72.a1', '108.b1', '108.o2', '108.w1', '108.bd1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2505, -1, 9388, -1], 'generators': [9300, 12312, 3240, 12320, 5832, 5928], 'label': '17496.ro.36.k2', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.k2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k2', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833663
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '216.cm1', '216.co1', '216.cq1', '324.q1'], 'contains': ['1944.c1', '1944.r1', '1944.u1', '1944.ba1', '1944.bx1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [2292, -1, 4373, -1], 'generators': [12320, 7200, 5832], 'label': '17496.ro.648.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.bn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833664
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '216.cr1', '216.cs1', '216.ct1', '324.r1'], 'contains': ['1944.m1', '1944.n1', '1944.o1', '1944.bo1', '1944.bp1', '1944.by1', '1944.bz1', '1944.ca1', '1944.cb1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [5506, -1, 4006, -1], 'generators': [11672, 10584, 5832], 'label': '17496.ro.648.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.bo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833665
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.c1', '216.cr1', '216.cu1', '216.cv1', '216.cw1', '324.s1'], 'contains': ['1944.m1', '1944.p1', '1944.s1', '1944.bq1', '1944.cc1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [4132, -1, 6486, -1], 'generators': [11672, 15864, 5832], 'label': '17496.ro.648.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '648.bp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833666
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.d1', '216.cs1', '216.cu1', '216.cx1', '324.t1'], 'contains': ['1944.m1', '1944.q1', '1944.t1', '1944.br1', '1944.cd1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [1128, -1, 4775, -1], 'generators': [11672, 6720, 5832], 'label': '17496.ro.648.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.bq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833667
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '216.ct1', '216.cv1', '216.cx1', '324.u1'], 'contains': ['1944.m1', '1944.r1', '1944.u1', '1944.bs1', '1944.ce1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [2486, -1, 4350, -1], 'generators': [11672, 7200, 5832], 'label': '17496.ro.648.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.br1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833668
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '216.ck1', '216.cr1'], 'contains': ['1944.n1', '1944.o1', '1944.s1', '1944.ci1', '1944.cl1', '1944.cr1', '1944.cu1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [6127, -1, 4460, -1], 'generators': [5192, 456, 5832], 'label': '17496.ro.648.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.bs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833669
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '216.cl1', '216.cs1'], 'contains': ['1944.n1', '1944.o1', '1944.t1', '1944.cj1', '1944.cm1', '1944.cs1', '1944.cv1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3722, -1, 3890, -1], 'generators': [9512, 4488, 5832], 'label': '17496.ro.648.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.bt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833670
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.h1', '216.cm1', '216.ct1'], 'contains': ['1944.n1', '1944.o1', '1944.u1', '1944.ck1', '1944.cn1', '1944.ct1', '1944.cw1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4840, -1, 3361, -1], 'generators': [9512, 456, 5832], 'label': '17496.ro.648.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.bu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833671
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '216.ck1', '216.cr1', '324.bm1'], 'contains': ['1944.n1', '1944.p1', '1944.cf1', '1944.co1', '1944.cx1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [5681, -1, 5625, -1], 'generators': [15360, 9792, 5832], 'label': '17496.ro.648.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.bv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833672
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.cl1', '216.cs1', '324.bn1'], 'contains': ['1944.n1', '1944.q1', '1944.cg1', '1944.cp1', '1944.cy1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2234, -1, 4191, -1], 'generators': [9528, 14328, 5832], 'label': '17496.ro.648.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '648.bw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bw1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833673
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '18.g1'], 'contains': ['72.m1', '108.c1', '108.d1', '108.p1', '108.bm1', '108.bt1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [713, -1, 6928, -1], 'generators': [9300, 5832, 7200, 12320, 648, 6720], 'label': '17496.ro.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '36.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833674
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '216.cm1', '216.ct1', '324.bo1'], 'contains': ['1944.n1', '1944.r1', '1944.ch1', '1944.cq1', '1944.cz1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3399, -1, 3639, -1], 'generators': [12120, 16416, 5832], 'label': '17496.ro.648.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.bx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bx1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833675
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ba1', '216.ck1', '216.cr1'], 'contains': ['1944.o1', '1944.p1', '1944.s1', '1944.da1', '1944.dd1', '1944.dd2', '1944.dg1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [5957, -1, 5715, -1], 'generators': [7784, 10824, 5832], 'label': '17496.ro.648.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.by1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833676
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bb1', '216.cl1', '216.cs1'], 'contains': ['1944.o1', '1944.q1', '1944.t1', '1944.db1', '1944.de1', '1944.de2', '1944.dh1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1246, -1, 3983, -1], 'generators': [9512, 12048, 5832], 'label': '17496.ro.648.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.bz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833677
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bc1', '216.cm1', '216.ct1'], 'contains': ['1944.o1', '1944.r1', '1944.u1', '1944.dc1', '1944.df1', '1944.df2', '1944.di1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3925, -1, 3431, -1], 'generators': [9512, 11040, 5832], 'label': '17496.ro.648.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.ca1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833678
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.be1', '216.cn1', '216.cu1'], 'contains': ['1944.p1', '1944.s1', '1944.t1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [3130, -1, 6464, -1], 'generators': [12536, 15648], 'label': '17496.ro.648.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '648.cb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cb1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833679
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bf1', '216.co1', '216.cv1'], 'contains': ['1944.p1', '1944.s1', '1944.u1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [3240, -1, 5737, -1], 'generators': [80, 4704], 'label': '17496.ro.648.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.k1', 'old_label': '648.cc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cc1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833680
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bg2', '216.cp1', '216.cw1'], 'contains': ['1944.p1', '1944.s1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [4174, -1, 8013, -1], 'generators': [5192, 6984], 'label': '17496.ro.648.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.l1', 'old_label': '648.cd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cd1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833681
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bi1', '216.cn1', '216.cu1', '324.bp1'], 'contains': ['1944.p1', '1944.q1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1770, -1, 6507, -1], 'generators': [5712, 6048], 'label': '17496.ro.648.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '648.ce1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ce1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833682
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bj1', '216.co1', '216.cv1', '324.bq1'], 'contains': ['1944.p1', '1944.r1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2661, -1, 5465, -1], 'generators': [5208, 7200], 'label': '17496.ro.648.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '648.cf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cf1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833683
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bk1', '216.cp1', '216.cw1', '324.br1'], 'contains': ['1944.p1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3801, -1, 8225, -1], 'generators': [2448, 3240], 'label': '17496.ro.648.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '648.cg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833684
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '27.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [919, -1, 8918, -1], 'generators': [3469, 5832, 4824, 12528, 6, 9240, 12312, 14256, 9300], 'label': '17496.ro.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '1944.3559'}
  • id: 157833685
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.h1'], 'contains': ['72.n1', '108.c1', '108.q1', '108.x1', '108.be1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [243, -1, 7941, -1], 'generators': [1956, 12312, 6696, 12320, 5832, 7728], 'label': '17496.ro.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '36.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833686
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bl1', '216.cn1', '216.cu1'], 'contains': ['1944.q1', '1944.s1', '1944.t1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [1113, -1, 5798, -1], 'generators': [10256, 216], 'label': '17496.ro.648.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '648.ch1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ch1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833687
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bn1', '216.cq1', '216.cx1'], 'contains': ['1944.q1', '1944.t1', '1944.u1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [1142, -1, 4620, -1], 'generators': [15200, 11832], 'label': '17496.ro.648.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.m1', 'old_label': '648.ci1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ci1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833688
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bp1', '216.cq1', '216.cx1', '324.bs1'], 'contains': ['1944.q1', '1944.r1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [954, -1, 4754, -1], 'generators': [888, 13032], 'label': '17496.ro.648.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '648.cj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cj1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833691
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.cy1', '216.cz1', '216.da1', '216.df1', '216.dg1', '216.dh1', '324.v1'], 'contains': ['1944.v1', '1944.w1', '1944.x1', '1944.bc1', '1944.bf1', '1944.by1', '1944.ca1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [6568, -1, 3315, -1], 'generators': [12320, 4104, 6480], 'label': '17496.ro.648.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.cm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833692
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.db1', '216.dc1', '216.dd1', '216.de1', '216.df1', '216.dg1', '216.dh1', '216.di1', '324.w1'], 'contains': ['1944.v1', '1944.w1', '1944.bd1', '1944.bh1', '1944.bz1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [8578, -1, 2886, -1], 'generators': [12320, 9936, 648], 'label': '17496.ro.648.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.cn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833693
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.cy1', '216.cz1', '216.da1', '216.db1', '216.dj1', '216.dk1', '216.dl1'], 'contains': ['1944.v1', '1944.x1', '1944.be1', '1944.bg1', '1944.cb1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [6729, -1, 2447, -1], 'generators': [12320, 15768, 648], 'label': '17496.ro.648.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.co1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.co1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833694
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.c1', '216.cy1', '216.dc1', '216.dd1', '216.de1', '216.df1', '216.dj1', '216.dk1', '216.dl1', '324.x1'], 'contains': ['1944.v1', '1944.y1', '1944.bi1', '1944.bl1', '1944.cc1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [8593, -1, 2834, -1], 'generators': [12320, 15864, 6480], 'label': '17496.ro.648.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.cp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833695
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.d1', '216.cz1', '216.dc1', '216.dd1', '216.dg1', '216.dj1', '216.dk1', '324.y1'], 'contains': ['1944.v1', '1944.z1', '1944.bj1', '1944.bm1', '1944.cd1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [3502, -1, 2944, -1], 'generators': [12320, 888, 6480], 'label': '17496.ro.648.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.cq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833696
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.i1'], 'contains': ['72.o1', '108.d1', '108.r1', '108.y1', '108.bf1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1517, -1, 5615, -1], 'generators': [5052, 12312, 2880, 12320, 5832, 10392], 'label': '17496.ro.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833697
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '216.da1', '216.dc1', '216.de1', '216.dh1', '216.dj1', '216.dl1', '324.z1'], 'contains': ['1944.v1', '1944.ba1', '1944.bk1', '1944.bn1', '1944.ce1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [6629, -1, 2650, -1], 'generators': [12320, 15576, 6480], 'label': '17496.ro.648.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.cr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833698
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bw1', '216.ck1', '216.cy1', '216.df1'], 'contains': ['1944.w1', '1944.x1', '1944.y1', '1944.cf1', '1944.ci1', '1944.cu1', '1944.da1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 288, 'diagramx': [6553, -1, 4529, -1], 'generators': [12320, 14064, 14904], 'label': '17496.ro.648.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.cs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833699
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.cl1', '216.cz1', '216.dg1'], 'contains': ['1944.w1', '1944.x1', '1944.z1', '1944.cg1', '1944.cj1', '1944.cv1', '1944.db1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [3685, -1, 3867, -1], 'generators': [12320, 15360, 2664], 'label': '17496.ro.648.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.ct1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ct1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833700
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.by1', '216.cm1', '216.da1', '216.dh1'], 'contains': ['1944.w1', '1944.x1', '1944.ba1', '1944.ch1', '1944.ck1', '1944.cw1', '1944.dc1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [4331, -1, 3246, -1], 'generators': [12320, 1104, 10584], 'label': '17496.ro.648.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.cu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833701
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bw1', '216.ck1', '216.df1', '324.bt1'], 'contains': ['1944.w1', '1944.y1', '1944.cl1', '1944.co1', '1944.dg1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [6438, -1, 5579, -1], 'generators': [12320, 14064, 15624], 'label': '17496.ro.648.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.cv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833702
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.cl1', '216.dg1', '324.bu1'], 'contains': ['1944.w1', '1944.z1', '1944.cm1', '1944.cp1', '1944.dh1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [2213, -1, 4122, -1], 'generators': [12320, 15360, 2016], 'label': '17496.ro.648.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '648.cw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cw1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833703
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.by1', '216.cm1', '216.dh1', '324.bv1'], 'contains': ['1944.w1', '1944.ba1', '1944.cn1', '1944.cq1', '1944.di1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4485, -1, 3500, -1], 'generators': [12320, 456, 10584], 'label': '17496.ro.648.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.cx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cx1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833704
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bw1', '216.ck1', '216.cy1'], 'contains': ['1944.x1', '1944.y1', '1944.cr1', '1944.cx1', '1944.dd1', '1944.dd2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 288, 'diagramx': [5920, -1, 5510, -1], 'generators': [12320, 2400, 15624], 'label': '17496.ro.648.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.cy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833705
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.cl1', '216.cz1'], 'contains': ['1944.x1', '1944.z1', '1944.cs1', '1944.cy1', '1944.de1', '1944.de2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [1851, -1, 3937, -1], 'generators': [12320, 3696, 2664], 'label': '17496.ro.648.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.cz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833706
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.by1', '216.cm1', '216.da1'], 'contains': ['1944.x1', '1944.ba1', '1944.ct1', '1944.cz1', '1944.df1', '1944.df2'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [3909, -1, 3153, -1], 'generators': [12320, 1104, 16416], 'label': '17496.ro.648.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.da1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.da1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833707
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.b1'], 'contains': ['72.bd1', '108.e1', '108.g1', '108.j1', '108.l1', '108.n1', '108.p1', '108.r1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2544, -1, 6687, -1], 'generators': [9300, 5832, 648, 14712, 7200, 9288], 'label': '17496.ro.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833708
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '216.dm1', '216.dn1', '216.do1', '216.dt1', '216.du1', '216.dv1', '324.ba1'], 'contains': ['1944.bb1', '1944.bc1', '1944.bf1', '1944.bo1', '1944.bp1', '1944.bt1', '1944.bu1', '1944.bz1', '1944.cb1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5837, -1, 3593, -1], 'generators': [6488, 4104, 6480], 'label': '17496.ro.648.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.db1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.db1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833709
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '216.dp1', '216.dq1', '216.dr1', '216.ds1', '216.dt1', '216.du1', '216.dv1', '216.dw1', '324.bb1'], 'contains': ['1944.bb1', '1944.bd1', '1944.bg1', '1944.bo1', '1944.bt1', '1944.by1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6976, -1, 3269, -1], 'generators': [656, 14712, 648], 'label': '17496.ro.648.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.dc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833710
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '216.dm1', '216.dn1', '216.do1', '216.dp1', '216.dx1', '216.dy1', '216.dz1'], 'contains': ['1944.bb1', '1944.be1', '1944.bg1', '1944.bh1', '1944.bp1', '1944.bu1', '1944.ca1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6961, -1, 2378, -1], 'generators': [6488, 15768, 648], 'label': '17496.ro.648.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.dd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dd1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833711
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.c1', '216.dm1', '216.dq1', '216.dr1', '216.ds1', '216.dt1', '216.dx1', '216.dy1', '216.dz1', '324.bc1'], 'contains': ['1944.bb1', '1944.bi1', '1944.bl1', '1944.bq1', '1944.bv1', '1944.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7137, -1, 3384, -1], 'generators': [656, 15864, 6480], 'label': '17496.ro.648.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.de1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.de1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833712
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.d1', '216.dn1', '216.dq1', '216.dr1', '216.du1', '216.dx1', '216.dy1', '324.bd1'], 'contains': ['1944.bb1', '1944.bj1', '1944.bm1', '1944.br1', '1944.bw1', '1944.cd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [2098, -1, 3292, -1], 'generators': [6488, 888, 6480], 'label': '17496.ro.648.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.df1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.df1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833713
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.e1', '216.do1', '216.dq1', '216.ds1', '216.dv1', '216.dx1', '216.dz1', '324.be1'], 'contains': ['1944.bb1', '1944.bk1', '1944.bn1', '1944.bs1', '1944.bx1', '1944.ce1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6208, -1, 2731, -1], 'generators': [6488, 15576, 6480], 'label': '17496.ro.648.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.dg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833714
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.f1', '216.cy1', '216.dm1', '216.dt1', '216.ea2', '216.ea3', '216.eb1', '216.eb2', '216.ec1', '216.ec2', '216.ek1', '216.el1', '216.em1'], 'contains': ['1944.bc1', '1944.bg1', '1944.bl1', '1944.ci1', '1944.cr1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7597, -1, 2196, -1], 'generators': [16856, 456, 648], 'label': '17496.ro.648.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833715
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.g1', '216.cz1', '216.dn1', '216.du1', '216.ea1', '216.ea3', '216.ec1', '216.ek1', '216.em1'], 'contains': ['1944.bc1', '1944.bg1', '1944.bm1', '1944.cj1', '1944.cs1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6614, -1, 2401, -1], 'generators': [3680, 4488, 648], 'label': '17496.ro.648.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.di1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.di1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833716
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.h1', '216.da1', '216.do1', '216.dv1', '216.ea1', '216.ea2', '216.eb1', '216.ek1', '216.el1'], 'contains': ['1944.bc1', '1944.bg1', '1944.bn1', '1944.ck1', '1944.ct1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7463, -1, 2262, -1], 'generators': [3680, 456, 648], 'label': '17496.ro.648.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dj1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833717
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '216.df1', '216.dm1', '216.ea1', '216.eb1', '216.ec1', '216.en1', '216.eo1', '216.ep1'], 'contains': ['1944.bc1', '1944.bh1', '1944.bl1', '1944.cl1', '1944.cu1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8726, -1, 2583, -1], 'generators': [5192, 15360, 6480], 'label': '17496.ro.648.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dk1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833718
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.c1'], 'contains': ['72.be1', '108.e1', '108.f1', '108.i1', '108.l1', '108.m1', '108.p1', '108.q1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2280, -1, 7316, -1], 'generators': [9300, 5832, 648, 14712, 2016, 6696], 'label': '17496.ro.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '36.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833719
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '216.dg1', '216.dn1', '216.ea2', '216.ec2', '216.en1', '216.ep1'], 'contains': ['1944.bc1', '1944.bh1', '1944.bm1', '1944.cm1', '1944.cv1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6844, -1, 2355, -1], 'generators': [9512, 4488, 648], 'label': '17496.ro.648.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dl1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833720
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.h1', '216.dh1', '216.do1', '216.ea3', '216.eb2', '216.en1', '216.eo1'], 'contains': ['1944.bc1', '1944.bh1', '1944.bn1', '1944.cn1', '1944.cw1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7548, -1, 2285, -1], 'generators': [9512, 456, 648], 'label': '17496.ro.648.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833721
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.p1', '216.cy1', '216.dm1', '216.ea1', '216.ea2', '216.ea3', '216.eq1', '216.eq2', '216.eq3'], 'contains': ['1944.bc1', '1944.be1', '1944.bi1', '1944.cf1', '1944.cx1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7106, -1, 2560, -1], 'generators': [14712, 14904, 6480], 'label': '17496.ro.648.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dn1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833722
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.cz1', '216.dn1', '216.eb1', '216.eb2', '216.eq1', '216.eq3'], 'contains': ['1944.bc1', '1944.be1', '1944.bj1', '1944.cg1', '1944.cy1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4989, -1, 2537, -1], 'generators': [2400, 2016, 648], 'label': '17496.ro.648.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.do1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.do1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833723
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '216.da1', '216.do1', '216.ec1', '216.ec2', '216.eq1', '216.eq2'], 'contains': ['1944.bc1', '1944.be1', '1944.bk1', '1944.ch1', '1944.cz1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6599, -1, 2239, -1], 'generators': [1752, 17064, 648], 'label': '17496.ro.648.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dp1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833724
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.s1', '216.db1', '216.dp1', '216.ed1', '216.ed2', '216.ed3', '216.eq1', '216.eq2', '216.eq3'], 'contains': ['1944.bd1', '1944.be1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7562, -1, 984, -1], 'generators': [14712, 16416], 'label': '17496.ro.648.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.dq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dq1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833725
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '216.df1', '216.dt1', '216.ed1', '216.ee1', '216.eh1', '216.er1'], 'contains': ['1944.bd1', '1944.bf1', '1944.bl1', '1944.ci1', '1944.cl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8608, -1, 2606, -1], 'generators': [5192, 15360, 648], 'label': '17496.ro.648.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dr1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833726
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '216.dg1', '216.du1', '216.ed2', '216.eg1', '216.ej1', '216.er1'], 'contains': ['1944.bd1', '1944.bf1', '1944.bm1', '1944.cj1', '1944.cm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7342, -1, 2494, -1], 'generators': [9512, 16152, 6480], 'label': '17496.ro.648.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ds1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ds1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833727
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.h1', '216.dh1', '216.dv1', '216.ed3', '216.ef1', '216.ei1', '216.er1'], 'contains': ['1944.bd1', '1944.bf1', '1944.bn1', '1944.ck1', '1944.cn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7896, -1, 2309, -1], 'generators': [9512, 456, 6480], 'label': '17496.ro.648.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dt1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833847
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.m1', '324.q1', '324.be1', '324.ci1'], 'contains': ['1944.bx1', '2916.f1', '2916.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1766, -1, 5182, -1], 'generators': [9300, 6488, 5208], 'label': '17496.ro.972.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.bf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833728
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.i1', '216.db1', '216.dp1', '216.dw1', '216.eh1', '216.ei1', '216.ej1', '216.ek1', '216.el1', '216.em1'], 'contains': ['1944.bd1', '1944.bg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9230, -1, 1795, -1], 'generators': [15344, 15360], 'label': '17496.ro.648.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.du1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.du1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833729
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.d1'], 'contains': ['72.bf1', '108.e1', '108.f1', '108.g1', '108.h1', '108.l1', '108.m1', '108.n1', '108.o1', '108.o2'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2927, -1, 7366, -1], 'generators': [9300, 5832, 648, 14712, 16272, 9288], 'label': '17496.ro.36.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '36.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833730
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.i1', '216.di1', '216.dp1', '216.ee1', '216.ef1', '216.eg1', '216.en1', '216.eo1', '216.ep1'], 'contains': ['1944.bd1', '1944.bh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9989, -1, 1855, -1], 'generators': [9512, 15360], 'label': '17496.ro.648.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.dv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dv1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833731
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.j1', '216.dc1', '216.dq1', '216.ee1', '216.eh1', '216.eq1', '216.es1', '324.bw1'], 'contains': ['1944.bd1', '1944.bi1', '1944.bj1', '1944.bk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8174, -1, 2628, -1], 'generators': [16008, 7200], 'label': '17496.ro.648.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.dw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dw1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833732
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.k1', '216.dd1', '216.dr1', '216.ef1', '216.ei1', '216.eq3', '216.es1', '324.bx1'], 'contains': ['1944.bd1', '1944.bi1', '1944.bj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8564, -1, 2672, -1], 'generators': [10176, 9936], 'label': '17496.ro.648.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.dx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dx1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833733
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.l1', '216.de1', '216.ds1', '216.eg1', '216.ej1', '216.eq2', '216.es1', '324.by1'], 'contains': ['1944.bd1', '1944.bi1', '1944.bk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8550, -1, 2515, -1], 'generators': [6360, 9936], 'label': '17496.ro.648.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.dy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dy1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833734
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.m1', '216.dc1', '216.dq1', '216.ed1', '216.ee1', '216.eh1', '216.ek1', '216.en1', '216.er1'], 'contains': ['1944.bd1', '1944.bl1', '1944.bm1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9256, -1, 2084, -1], 'generators': [7280, 16152], 'label': '17496.ro.648.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.dz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dz1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833735
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.n1', '216.dd1', '216.dr1', '216.ed3', '216.ef1', '216.ei1', '216.em1', '216.ep1', '216.er1'], 'contains': ['1944.bd1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9715, -1, 2218, -1], 'generators': [2528, 15360], 'label': '17496.ro.648.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ea1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ea1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833736
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.o1', '216.de1', '216.ds1', '216.ed2', '216.eg1', '216.ej1', '216.el1', '216.eo1', '216.er1'], 'contains': ['1944.bd1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9655, -1, 2064, -1], 'generators': [1832, 10584], 'label': '17496.ro.648.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eb1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833737
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.p1', '216.df1', '216.dt1', '216.ek1', '216.en1', '216.eq1', '216.es1', '324.bz1'], 'contains': ['1944.bc1', '1944.bd1', '1944.bi1', '1944.cf1', '1944.co1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7495, -1, 3569, -1], 'generators': [3048, 15624, 6480], 'label': '17496.ro.648.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.ec1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ec1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833738
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.dg1', '216.du1', '216.el1', '216.eo1', '216.eq2', '216.es1', '324.ca1'], 'contains': ['1944.bc1', '1944.bd1', '1944.bj1', '1944.cg1', '1944.cp1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5026, -1, 2967, -1], 'generators': [5784, 9936, 648], 'label': '17496.ro.648.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.ed1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ed1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833739
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '216.dh1', '216.dv1', '216.em1', '216.ep1', '216.eq3', '216.es1', '324.cb1'], 'contains': ['1944.bc1', '1944.bd1', '1944.bk1', '1944.ch1', '1944.cq1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6645, -1, 2811, -1], 'generators': [1752, 11232, 648], 'label': '17496.ro.648.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '648.ee1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ee1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833740
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.e1'], 'contains': ['72.bj1', '108.e1', '108.f1', '108.g1', '108.h1', '108.i1', '108.j1', '108.k1', '108.ci1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4395, -1, 6555, -1], 'generators': [9300, 648, 9936, 5832, 14712, 7200], 'label': '17496.ro.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '36.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833741
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.s1', '216.di1', '216.dw1', '216.er1', '216.es1', '324.cc1'], 'contains': ['1944.bd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9847, -1, 2692, -1], 'generators': [14712, 10584], 'label': '17496.ro.648.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '648.ef1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ef1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833742
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.f1', '216.cy1', '216.dm1', '216.ed1', '216.ed2', '216.ed3', '216.et1', '216.et2', '216.et3'], 'contains': ['1944.be1', '1944.bf1', '1944.bl1', '1944.cr1', '1944.cu1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7912, -1, 1900, -1], 'generators': [5192, 9528, 648], 'label': '17496.ro.648.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eg1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833743
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.g1', '216.cz1', '216.dn1', '216.ed1', '216.ed3', '216.ev1', '216.ev2'], 'contains': ['1944.be1', '1944.bf1', '1944.bm1', '1944.cs1', '1944.cv1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6193, -1, 1877, -1], 'generators': [9512, 10320, 6480], 'label': '17496.ro.648.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833744
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.h1', '216.da1', '216.do1', '216.ed1', '216.ed2', '216.eu1', '216.eu2'], 'contains': ['1944.be1', '1944.bf1', '1944.bn1', '1944.ct1', '1944.cw1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6862, -1, 1381, -1], 'generators': [9512, 12120, 6480], 'label': '17496.ro.648.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ei1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ei1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833745
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.i1', '216.db1', '216.dp1', '216.ea1', '216.eb2', '216.ec2', '216.et1', '216.eu2', '216.ev2'], 'contains': ['1944.be1', '1944.bg1', '1944.bh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [8509, -1, 759, -1], 'generators': [15344, 9528], 'label': '17496.ro.648.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.ej1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ej1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833746
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ej2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.i1', '216.db1', '216.dp1', '216.ea2', '216.ea3', '216.eb1', '216.ec1', '216.et2', '216.et3', '216.eu1', '216.ev1'], 'contains': ['1944.be1', '1944.bg1', '1944.bh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [8496, -1, 810, -1], 'generators': [5456, 16416], 'label': '17496.ro.648.ej2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.ej2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ej2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833747
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.j1', '216.dj1', '216.dx1', '216.eq1', '216.eq2', '216.eq3', '216.et1', '216.et2', '216.et3'], 'contains': ['1944.be1', '1944.bi1', '1944.bj1', '1944.bk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7328, -1, 1774, -1], 'generators': [3048, 2232], 'label': '17496.ro.648.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ek1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ek1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833748
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.k1', '216.dk1', '216.dy1', '216.eq1', '216.eq2', '216.eu1', '216.eu2'], 'contains': ['1944.be1', '1944.bi1', '1944.bj1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7075, -1, 2024, -1], 'generators': [10176, 15768], 'label': '17496.ro.648.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.el1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.el1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833749
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.l1', '216.dl1', '216.dz1', '216.eq1', '216.eq3', '216.ev1', '216.ev2'], 'contains': ['1944.be1', '1944.bi1', '1944.bk1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7356, -1, 1734, -1], 'generators': [6360, 15768], 'label': '17496.ro.648.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.em1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.em1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833750
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.m1', '216.dj1', '216.dx1', '216.ea1', '216.ea2', '216.ea3', '216.ed1', '216.ed2', '216.ed3', '216.et1', '216.et2', '216.et3'], 'contains': ['1944.be1', '1944.bl1', '1944.bm1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [7852, -1, 1045, -1], 'generators': [7280, 10320], 'label': '17496.ro.648.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.en1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.en1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833751
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1'], 'contains': ['72.bx1', '108.bu1', '108.bv1', '108.bw1', '108.bx1', '108.by1', '108.bz1', '108.ca1', '108.ci1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [4478, -1, 5775, -1], 'generators': [9300, 648, 3240, 12320, 14712, 9936], 'label': '17496.ro.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '36.s1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833752
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.n1', '216.dk1', '216.dy1', '216.ec1', '216.ec2', '216.ed1', '216.ed2', '216.eu1', '216.eu2'], 'contains': ['1944.be1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7370, -1, 1025, -1], 'generators': [2528, 9528], 'label': '17496.ro.648.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eo1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833753
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.o1', '216.dl1', '216.dz1', '216.eb1', '216.eb2', '216.ed1', '216.ed3', '216.ev1', '216.ev2'], 'contains': ['1944.be1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7882, -1, 1004, -1], 'generators': [1832, 4752], 'label': '17496.ro.648.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ep1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ep1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833754
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.ba1', '216.df1', '216.dm1', '216.ee1', '216.ef1', '216.eg1', '216.et1', '216.eu1', '216.ev1'], 'contains': ['1944.bf1', '1944.bh1', '1944.bi1', '1944.bl1', '1944.da1', '1944.dg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8992, -1, 2470, -1], 'generators': [4616, 7008, 6480], 'label': '17496.ro.648.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eq1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833755
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bb1', '216.dg1', '216.dn1', '216.ee1', '216.ef1', '216.et2', '216.eu2'], 'contains': ['1944.bf1', '1944.bh1', '1944.bj1', '1944.bm1', '1944.db1', '1944.dh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5075, -1, 2332, -1], 'generators': [9512, 12048, 6480], 'label': '17496.ro.648.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.er1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.er1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833756
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bc1', '216.dh1', '216.do1', '216.ee1', '216.eg1', '216.et3', '216.ev2'], 'contains': ['1944.bf1', '1944.bh1', '1944.bk1', '1944.bn1', '1944.dc1', '1944.di1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7532, -1, 2126, -1], 'generators': [15344, 11040, 6480], 'label': '17496.ro.648.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.es1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.es1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833757
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.t1', '216.dk1', '216.dr1', '216.dy1', '216.ea1', '216.ea2', '216.eh1', '216.ej1', '216.ek1', '216.et1', '216.et2', '216.ev1'], 'contains': ['1944.bg1', '1944.bi1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8536, -1, 1983, -1], 'generators': [4832, 7224], 'label': '17496.ro.648.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.et1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.et1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833758
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.u1', '216.dl1', '216.ds1', '216.dz1', '216.ea1', '216.ea3', '216.eh1', '216.ei1', '216.ek1', '216.et1', '216.et3', '216.eu1'], 'contains': ['1944.bg1', '1944.bi1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8522, -1, 1942, -1], 'generators': [3680, 15648], 'label': '17496.ro.648.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.eu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eu1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833759
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.v1', '216.dj1', '216.dq1', '216.dx1', '216.ea2', '216.ea3', '216.ei1', '216.ej1', '216.ek1', '216.eu1', '216.eu2', '216.ev1', '216.ev2'], 'contains': ['1944.bg1', '1944.bi1', '1944.bm1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8053, -1, 1423, -1], 'generators': [13112, 10824], 'label': '17496.ro.648.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ev1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ev1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833760
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.w1', '216.dj1', '216.dq1', '216.dx1', '216.eb1', '216.eb2', '216.eh1', '216.ei1', '216.el1', '216.et2', '216.et3', '216.eu1', '216.eu2'], 'contains': ['1944.bg1', '1944.bj1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [8160, -1, 1922, -1], 'generators': [5912, 17376], 'label': '17496.ro.648.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ew1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ew1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833761
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.x1', '216.dk1', '216.dr1', '216.dy1', '216.eb1', '216.eh1', '216.el1', '216.et1', '216.et2'], 'contains': ['1944.bg1', '1944.bj1', '1944.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8147, -1, 2044, -1], 'generators': [17120, 15840], 'label': '17496.ro.648.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ex1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ex1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833762
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1'], 'contains': ['72.bz1', '108.cb1', '108.cc1', '108.cd1', '108.ce1', '108.cf1', '108.cg1', '108.ch1', '108.ci1'], 'core': '17496.a1', 'coset_action_label': '36T10908', 'count': 48, 'diagramx': [4436, -1, 6066, -1], 'generators': [9300, 648, 3240, 6488, 14712, 9936], 'label': '17496.ro.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '36.t1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157833763
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.y1', '216.dj1', '216.dq1', '216.dx1', '216.ec1', '216.ec2', '216.eh1', '216.ej1', '216.em1', '216.et2', '216.et3', '216.ev1', '216.ev2'], 'contains': ['1944.bg1', '1944.bk1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [7801, -1, 1403, -1], 'generators': [2216, 7200], 'label': '17496.ro.648.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ey1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ey1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833764
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.z1', '216.dl1', '216.ds1', '216.dz1', '216.ec1', '216.eh1', '216.em1', '216.et1', '216.et3'], 'contains': ['1944.bg1', '1944.bk1', '1944.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8301, -1, 1514, -1], 'generators': [17072, 2904], 'label': '17496.ro.648.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ez1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ez1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833765
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.ba1', '216.cy1', '216.dm1', '216.dt1', '216.eh1', '216.ei1', '216.ej1', '216.et2', '216.et3', '216.eu1', '216.eu2', '216.ev1', '216.ev2'], 'contains': ['1944.bf1', '1944.bg1', '1944.bi1', '1944.bl1', '1944.da1', '1944.dd1', '1944.dd2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [7962, -1, 2150, -1], 'generators': [17120, 14904, 6480], 'label': '17496.ro.648.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fa1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fa1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833766
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.bb1', '216.cz1', '216.dn1', '216.du1', '216.eh1', '216.ei1', '216.et1', '216.et3', '216.eu1'], 'contains': ['1944.bf1', '1944.bg1', '1944.bj1', '1944.bm1', '1944.db1', '1944.de1', '1944.de2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [3518, -1, 2424, -1], 'generators': [3680, 12048, 6480], 'label': '17496.ro.648.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fb1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833767
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.bc1', '216.da1', '216.do1', '216.dv1', '216.eh1', '216.ej1', '216.et1', '216.et2', '216.ev1'], 'contains': ['1944.bf1', '1944.bg1', '1944.bk1', '1944.bn1', '1944.dc1', '1944.df1', '1944.df2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7313, -1, 2173, -1], 'generators': [3680, 11040, 6480], 'label': '17496.ro.648.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fc1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833768
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.t1', '216.dd1', '216.dy1', '216.ea3', '216.ee1', '216.eg1', '216.en1', '216.et3', '216.ev2'], 'contains': ['1944.bh1', '1944.bi1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9391, -1, 2003, -1], 'generators': [10664, 7224], 'label': '17496.ro.648.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fd1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833769
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.u1', '216.de1', '216.dz1', '216.ea2', '216.ee1', '216.ef1', '216.en1', '216.et2', '216.eu2'], 'contains': ['1944.bh1', '1944.bi1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9270, -1, 1963, -1], 'generators': [9512, 15648], 'label': '17496.ro.648.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fe1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fe1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833770
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.v1', '216.dc1', '216.dx1', '216.ea1', '216.ef1', '216.eg1', '216.en1', '216.eu1', '216.ev1'], 'contains': ['1944.bh1', '1944.bi1', '1944.bm1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8978, -1, 1815, -1], 'generators': [1448, 10824], 'label': '17496.ro.648.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.ff1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ff1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833771
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.w1', '216.dc1', '216.dx1', '216.eb1', '216.ee1', '216.ef1', '216.eo1', '216.et1', '216.eu1'], 'contains': ['1944.bh1', '1944.bj1', '1944.bl1', '1944.bn1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9754, -1, 1835, -1], 'generators': [11744, 17376], 'label': '17496.ro.648.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fg1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833772
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.x1', '216.dd1', '216.dy1', '216.eb2', '216.ee1', '216.eo1', '216.et3'], 'contains': ['1944.bh1', '1944.bj1', '1944.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9864, -1, 2105, -1], 'generators': [5456, 15840], 'label': '17496.ro.648.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fh1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833773
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '18.a1'], 'contains': ['108.i1', '162.d1', '162.k1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [562, -1, 9156, -1], 'generators': [8155, 5832, 9144, 648, 8100, 10896], 'label': '17496.ro.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833774
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.y1', '216.dc1', '216.dx1', '216.ec1', '216.ee1', '216.eg1', '216.ep1', '216.et1', '216.ev1'], 'contains': ['1944.bh1', '1944.bk1', '1944.bl1', '1944.bm1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9243, -1, 1713, -1], 'generators': [13880, 7200], 'label': '17496.ro.648.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fi1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fi1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833775
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.z1', '216.de1', '216.dz1', '216.ec2', '216.ee1', '216.ep1', '216.et2'], 'contains': ['1944.bh1', '1944.bk1', '1944.bl1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9491, -1, 1754, -1], 'generators': [5408, 2904], 'label': '17496.ro.648.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '648.fj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fj1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157833776
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.bw1', '216.cr1', '216.dm1', '216.dt1'], 'contains': ['1944.bo1', '1944.bp1', '1944.bq1', '1944.cf1', '1944.ci1', '1944.cl1', '1944.cr1', '1944.da1', '1944.dd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6423, -1, 4599, -1], 'generators': [7136, 3048, 15624], 'label': '17496.ro.648.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.fk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833777
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bx1', '216.cs1', '216.dn1', '216.du1'], 'contains': ['1944.bo1', '1944.bp1', '1944.br1', '1944.cg1', '1944.cj1', '1944.cm1', '1944.cs1', '1944.db1', '1944.de1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3700, -1, 3821, -1], 'generators': [7136, 15360, 2664], 'label': '17496.ro.648.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.fl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833778
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.by1', '216.ct1', '216.do1', '216.dv1'], 'contains': ['1944.bo1', '1944.bp1', '1944.bs1', '1944.ch1', '1944.ck1', '1944.cn1', '1944.ct1', '1944.dc1', '1944.df1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5156, -1, 3223, -1], 'generators': [7136, 1104, 10584], 'label': '17496.ro.648.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.fm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833779
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bw1', '216.cr1', '216.dt1', '324.cd1'], 'contains': ['1944.bo1', '1944.bq1', '1944.ci1', '1944.co1', '1944.dd2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5904, -1, 5602, -1], 'generators': [7136, 15360, 14904], 'label': '17496.ro.648.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.fn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833780
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.cs1', '216.du1', '324.ce1'], 'contains': ['1944.bo1', '1944.br1', '1944.cj1', '1944.cp1', '1944.de2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2323, -1, 4214, -1], 'generators': [8, 456, 216], 'label': '17496.ro.648.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '648.fo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833781
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.by1', '216.ct1', '216.dv1', '324.cf1'], 'contains': ['1944.bo1', '1944.bs1', '1944.ck1', '1944.cq1', '1944.df2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4577, -1, 3523, -1], 'generators': [7136, 456, 10584], 'label': '17496.ro.648.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.fp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fp1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833782
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.bw1', '216.cr1', '216.dm1'], 'contains': ['1944.bp1', '1944.bq1', '1944.cr1', '1944.cu1', '1944.cx1', '1944.da1', '1944.dd2', '1944.dg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6335, -1, 4868, -1], 'generators': [7136, 2400, 15624], 'label': '17496.ro.648.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.fq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833783
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.bx1', '216.cs1', '216.dn1'], 'contains': ['1944.bp1', '1944.br1', '1944.cs1', '1944.cv1', '1944.cy1', '1944.db1', '1944.de2', '1944.dh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2064, -1, 3752, -1], 'generators': [7136, 6288, 216], 'label': '17496.ro.648.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.fr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833785
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.by1', '216.ct1', '216.do1'], 'contains': ['1944.bp1', '1944.bs1', '1944.ct1', '1944.cw1', '1944.cz1', '1944.dc1', '1944.df2', '1944.di1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4014, -1, 3084, -1], 'generators': [7136, 2400, 7200], 'label': '17496.ro.648.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.fs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833786
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cd1', '216.ck1', '216.dm1', '216.dt1'], 'contains': ['1944.bt1', '1944.bu1', '1944.bv1', '1944.cf1', '1944.ci1', '1944.cl1', '1944.cr1', '1944.da1', '1944.dd2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6387, -1, 4576, -1], 'generators': [656, 14064, 14904], 'label': '17496.ro.648.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.ft1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ft1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833787
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cl1', '216.dn1', '216.du1'], 'contains': ['1944.bt1', '1944.bu1', '1944.bw1', '1944.cg1', '1944.cj1', '1944.cm1', '1944.cs1', '1944.db1', '1944.de2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3669, -1, 3798, -1], 'generators': [6488, 15360, 2664], 'label': '17496.ro.648.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.fu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833788
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cf1', '216.cm1', '216.do1', '216.dv1'], 'contains': ['1944.bt1', '1944.bu1', '1944.bx1', '1944.ch1', '1944.ck1', '1944.cn1', '1944.ct1', '1944.dc1', '1944.df2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5212, -1, 3200, -1], 'generators': [6488, 1104, 10584], 'label': '17496.ro.648.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.fv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833789
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cd1', '216.ck1', '216.dt1', '324.cg1'], 'contains': ['1944.bt1', '1944.bv1', '1944.ci1', '1944.co1', '1944.dd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5982, -1, 5556, -1], 'generators': [656, 15360, 14904], 'label': '17496.ro.648.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.fw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833790
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cl1', '216.du1', '324.ch1'], 'contains': ['1944.bt1', '1944.bw1', '1944.cj1', '1944.cp1', '1944.de1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2198, -1, 4075, -1], 'generators': [6488, 15360, 2016], 'label': '17496.ro.648.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '648.fx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fx1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833791
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cf1', '216.cm1', '216.dv1', '324.ci1'], 'contains': ['1944.bt1', '1944.bx1', '1944.ck1', '1944.cq1', '1944.df1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4608, -1, 3477, -1], 'generators': [656, 456, 10584], 'label': '17496.ro.648.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '648.fy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fy1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833792
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cd1', '216.ck1', '216.dm1'], 'contains': ['1944.bu1', '1944.bv1', '1944.cr1', '1944.cu1', '1944.cx1', '1944.da1', '1944.dd1', '1944.dg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6370, -1, 4845, -1], 'generators': [6488, 2400, 15624], 'label': '17496.ro.648.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.fz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833793
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cl1', '216.dn1'], 'contains': ['1944.bu1', '1944.bw1', '1944.cs1', '1944.cv1', '1944.cy1', '1944.db1', '1944.de1', '1944.dh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1968, -1, 3728, -1], 'generators': [6488, 6288, 216], 'label': '17496.ro.648.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.ga1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ga1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833794
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cf1', '216.cm1', '216.do1'], 'contains': ['1944.bu1', '1944.bx1', '1944.ct1', '1944.cw1', '1944.cz1', '1944.dc1', '1944.df1', '1944.di1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4029, -1, 3061, -1], 'generators': [6488, 2400, 7200], 'label': '17496.ro.648.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.gb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833795
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.c1', '12.d1', '12.e1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1933, 3898, 7279, 2376], 'generators': [9300, 9936, 3240, 12320, 7200, 5832, 648, 14712], 'label': '17496.ro.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157833796
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '18.c1'], 'contains': ['108.k1', '162.p1', '486.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4114, -1, 6868, -1], 'generators': [3469, 648, 10584, 5832, 9300, 14712], 'label': '17496.ro.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1', 'old_label': '54.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833797
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cd1', '216.cr1', '216.df1', '216.dm1'], 'contains': ['1944.bz1', '1944.ca1', '1944.cc1', '1944.cf1', '1944.ci1', '1944.cl1', '1944.cu1', '1944.da1', '1944.dg1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [7061, -1, 4506, -1], 'generators': [11672, 14064, 14904], 'label': '17496.ro.648.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.gc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833798
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cs1', '216.dg1', '216.dn1'], 'contains': ['1944.bz1', '1944.ca1', '1944.cd1', '1944.cg1', '1944.cj1', '1944.cm1', '1944.cv1', '1944.db1', '1944.dh1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3744, -1, 3775, -1], 'generators': [11672, 15360, 2664], 'label': '17496.ro.648.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.gd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833799
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cf1', '216.ct1', '216.dh1', '216.do1'], 'contains': ['1944.bz1', '1944.ca1', '1944.ce1', '1944.ch1', '1944.ck1', '1944.cn1', '1944.cw1', '1944.dc1', '1944.di1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5645, -1, 3130, -1], 'generators': [11672, 1104, 10584], 'label': '17496.ro.648.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.ge1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ge1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833800
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cd1', '216.cr1', '216.cy1', '216.dt1'], 'contains': ['1944.by1', '1944.cb1', '1944.cc1', '1944.cf1', '1944.ci1', '1944.cr1', '1944.dd1', '1944.dd2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6537, -1, 4553, -1], 'generators': [1304, 14064, 14904], 'label': '17496.ro.648.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.gf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833801
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cs1', '216.cz1', '216.du1'], 'contains': ['1944.by1', '1944.cb1', '1944.cd1', '1944.cg1', '1944.cj1', '1944.cs1', '1944.de1', '1944.de2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3297, -1, 3844, -1], 'generators': [5840, 15360, 2664], 'label': '17496.ro.648.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.gg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833802
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cf1', '216.ct1', '216.da1', '216.dv1'], 'contains': ['1944.by1', '1944.cb1', '1944.ce1', '1944.ch1', '1944.ck1', '1944.ct1', '1944.df1', '1944.df2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5182, -1, 3176, -1], 'generators': [5840, 1104, 10584], 'label': '17496.ro.648.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.gh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833803
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cd1', '216.cr1', '216.df1', '216.dt1', '324.cj1'], 'contains': ['1944.by1', '1944.bz1', '1944.cc1', '1944.ci1', '1944.cl1', '1944.co1', '1944.da1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6584, -1, 4712, -1], 'generators': [11672, 14064, 15624], 'label': '17496.ro.648.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '648.gi1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833804
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.ce1', '216.cs1', '216.dg1', '216.du1', '324.ck1'], 'contains': ['1944.by1', '1944.bz1', '1944.cd1', '1944.cj1', '1944.cm1', '1944.cp1', '1944.db1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4704, -1, 3960, -1], 'generators': [11672, 456, 216], 'label': '17496.ro.648.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '648.gj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833805
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.cf1', '216.ct1', '216.dh1', '216.dv1', '324.cl1'], 'contains': ['1944.by1', '1944.bz1', '1944.ce1', '1944.ck1', '1944.cn1', '1944.cq1', '1944.dc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5666, -1, 3338, -1], 'generators': [11672, 456, 10584], 'label': '17496.ro.648.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '648.gk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833806
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['216.cd1', '216.cr1', '216.cy1', '216.dm1'], 'contains': ['1944.ca1', '1944.cb1', '1944.cc1', '1944.cr1', '1944.cu1', '1944.cx1', '1944.da1', '1944.dd1', '1944.dd2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': [6521, -1, 4642, -1], 'generators': [5840, 2400, 15624], 'label': '17496.ro.648.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.gl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833807
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '18.d1', '27.a1'], 'contains': ['108.o2', '162.f1', '486.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1271, -1, 9870, -1], 'generators': [3469, 12312, 4392, 5832, 9300, 1824], 'label': '17496.ro.54.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833808
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.ce1', '216.cs1', '216.cz1', '216.dn1'], 'contains': ['1944.ca1', '1944.cb1', '1944.cd1', '1944.cs1', '1944.cv1', '1944.cy1', '1944.db1', '1944.de1', '1944.de2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [3116, -1, 3705, -1], 'generators': [5840, 6288, 216], 'label': '17496.ro.648.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '648.gm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833809
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '648.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.cf1', '216.ct1', '216.da1', '216.do1'], 'contains': ['1944.ca1', '1944.cb1', '1944.ce1', '1944.ct1', '1944.cw1', '1944.cz1', '1944.dc1', '1944.df1', '1944.df2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [5112, -1, 3107, -1], 'generators': [5840, 2400, 7200], 'label': '17496.ro.648.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '648.gn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833810
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '729.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.b1', '243.a1', '243.b1'], 'contains': ['1458.a1', '1458.b1', '1458.c1', '2187.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [191, -1, 9973, -1], 'generators': [3469, 4914, 12312, 9300], 'label': '17496.ro.729.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '729.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833811
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '729.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['243.a1', '243.c1'], 'contains': ['1458.d1', '1458.e1', '1458.f1', '2187.a1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [334, -1, 9851, -1], 'generators': [3469, 4914, 9300, 5832], 'label': '17496.ro.729.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '729.b1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833812
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '729.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['243.b1', '243.c1'], 'contains': ['1458.g1', '1458.h1', '1458.i1', '2187.a1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 243, 'diagramx': [441, -1, 9731, -1], 'generators': [3469, 4914, 9300, 12320], 'label': '17496.ro.729.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '729.c1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833813
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '324.d1', '324.e1', '486.a1', '486.b1', '486.c1'], 'contains': ['1944.a1', '2916.a1', '2916.b1', '2916.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [897, -1, 8351, -1], 'generators': [9300, 648, 5832], 'label': '17496.ro.972.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833814
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.f1', '324.g1', '324.h1', '324.i1', '486.d1', '486.e1', '486.f1'], 'contains': ['1944.b1', '2916.a1', '2916.c1', '2916.e1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [1101, -1, 8313, -1], 'generators': [9300, 12312, 12320], 'label': '17496.ro.972.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833815
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.j1', '324.k1', '324.l1', '324.m1', '486.g1'], 'contains': ['1944.d1', '2916.a1', '2916.f1', '2916.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1620, -1, 8043, -1], 'generators': [9300, 12312, 656], 'label': '17496.ro.972.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '972.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833816
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.n1', '324.o1', '324.p1', '324.q1', '486.h1', '486.i1', '486.j1'], 'contains': ['1944.c1', '2916.b1', '2916.c1', '2916.f1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [1234, -1, 8274, -1], 'generators': [9300, 12320, 5832], 'label': '17496.ro.972.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.d1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833817
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.r1', '324.s1', '324.t1', '324.u1', '486.k1'], 'contains': ['1944.m1', '2916.b1', '2916.e1', '2916.g1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 162, 'diagramx': [1408, -1, 7946, -1], 'generators': [9300, 12968, 5832], 'label': '17496.ro.972.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1', 'old_label': '972.e1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833818
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '18.e1', '27.a1'], 'contains': ['108.o2', '162.g1', '486.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [998, -1, 9970, -1], 'generators': [6, 12312, 5832, 12, 8280, 8640], 'label': '17496.ro.54.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833819
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.v1', '324.w1', '324.x1', '324.y1', '324.z1', '486.l1'], 'contains': ['1944.v1', '2916.c1', '2916.d1', '2916.g1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 162, 'diagramx': [4506, -1, 6394, -1], 'generators': [9300, 648, 12320], 'label': '17496.ro.972.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '972.f1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833820
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.ba1', '324.bb1', '324.bc1', '324.bd1', '324.be1'], 'contains': ['1944.bb1', '2916.d1', '2916.e1', '2916.f1', '2916.g1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [4532, -1, 7255, -1], 'generators': [9300, 648, 656], 'label': '17496.ro.972.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '972.g1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833821
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.f1', '324.j1', '324.bf1', '324.bg1', '324.bh1'], 'contains': ['1944.e1', '2916.a1', '2916.h1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2914, -1, 7469, -1], 'generators': [9300, 12312, 14712], 'label': '17496.ro.972.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833822
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.c1', '324.g1', '324.k1', '324.bf1', '324.bi1', '324.bj1'], 'contains': ['1944.g1', '2916.a1', '2916.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2437, -1, 8389, -1], 'generators': [9300, 12312, 5928], 'label': '17496.ro.972.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833823
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.d1', '324.h1', '324.l1', '324.bg1', '324.bi1', '324.bk1'], 'contains': ['1944.h1', '2916.a1', '2916.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [167, -1, 7984, -1], 'generators': [9300, 12312, 6720], 'label': '17496.ro.972.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833824
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.e1', '324.i1', '324.m1', '324.bh1', '324.bi1', '324.bl1'], 'contains': ['1944.i1', '2916.a1', '2916.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1455, -1, 5360, -1], 'generators': [9300, 12312, 7200], 'label': '17496.ro.972.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833825
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.n1', '324.r1', '324.bm1', '324.bn1', '324.bo1'], 'contains': ['1944.n1', '2916.b1', '2916.h1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [2940, -1, 7432, -1], 'generators': [9300, 5832, 14712], 'label': '17496.ro.972.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.l1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833826
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.c1', '324.o1', '324.s1', '324.bm1', '324.bp1', '324.bq1', '324.br1'], 'contains': ['1944.p1', '2916.b1', '2916.i1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 432, 'diagramx': [2469, -1, 8195, -1], 'generators': [9300, 5832, 5928], 'label': '17496.ro.972.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.m1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833827
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.d1', '324.p1', '324.t1', '324.bn1', '324.bp1', '324.bs1'], 'contains': ['1944.q1', '2916.b1', '2916.j1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [825, -1, 7907, -1], 'generators': [9300, 5832, 6720], 'label': '17496.ro.972.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833828
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.e1', '324.q1', '324.u1', '324.bo1', '324.bq1', '324.bs1'], 'contains': ['1944.r1', '2916.b1', '2916.k1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 216, 'diagramx': [1525, -1, 5436, -1], 'generators': [9300, 5832, 7200], 'label': '17496.ro.972.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.o1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833829
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '18.f1', '27.a1'], 'contains': ['108.o2', '162.h1', '486.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1141, -1, 9806, -1], 'generators': [4255, 12312, 5832, 17292, 2688, 9072], 'label': '17496.ro.54.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833830
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '324.n1', '324.v1', '324.w1', '324.bt1', '324.bu1', '324.bv1'], 'contains': ['1944.w1', '2916.c1', '2916.h1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [3009, -1, 7332, -1], 'generators': [9300, 12320, 9936], 'label': '17496.ro.972.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.p1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833831
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.g1', '324.o1', '324.x1', '324.bt1'], 'contains': ['1944.y1', '2916.c1', '2916.i1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 432, 'diagramx': [2796, -1, 8157, -1], 'generators': [9300, 12320, 5928], 'label': '17496.ro.972.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.q1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833832
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.h1', '324.p1', '324.y1', '324.bu1'], 'contains': ['1944.z1', '2916.c1', '2916.j1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [962, -1, 7869, -1], 'generators': [9300, 12320, 6720], 'label': '17496.ro.972.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.r1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833833
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.i1', '324.q1', '324.z1', '324.bv1'], 'contains': ['1944.ba1', '2916.c1', '2916.k1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 216, 'diagramx': [1708, -1, 5296, -1], 'generators': [9300, 12320, 5208], 'label': '17496.ro.972.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.s1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833834
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.v1', '324.ba1', '324.bz1', '324.ca1', '324.cb1'], 'contains': ['1944.bc1', '2916.d1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [5098, -1, 6318, -1], 'generators': [9300, 6480, 14712], 'label': '17496.ro.972.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.t1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833835
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.w1', '324.bb1', '324.bw1', '324.bx1', '324.by1', '324.bz1', '324.ca1', '324.cb1', '324.cc1'], 'contains': ['1944.bd1', '2916.d1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [5358, -1, 5220, -1], 'generators': [9300, 648, 14712], 'label': '17496.ro.972.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.u1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833836
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['324.c1', '324.x1', '324.bc1', '324.bw1', '324.bx1', '324.by1', '324.bz1'], 'contains': ['1944.bi1', '2916.d1', '2916.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [5171, -1, 5398, -1], 'generators': [9300, 6480, 5928], 'label': '17496.ro.972.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.v1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833837
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.d1', '324.y1', '324.bd1', '324.bw1', '324.bx1', '324.ca1'], 'contains': ['1944.bj1', '2916.d1', '2916.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3365, -1, 6356, -1], 'generators': [9300, 6480, 6720], 'label': '17496.ro.972.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.w1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833838
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.e1', '324.z1', '324.be1', '324.bw1', '324.by1', '324.cb1'], 'contains': ['1944.bk1', '2916.d1', '2916.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5204, -1, 5105, -1], 'generators': [9300, 6480, 5208], 'label': '17496.ro.972.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.x1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833839
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.f1', '324.r1', '324.ba1', '324.bb1', '324.cd1', '324.ce1', '324.cf1'], 'contains': ['1944.bo1', '2916.e1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3073, -1, 7393, -1], 'generators': [9300, 7136, 9936], 'label': '17496.ro.972.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.y1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833840
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '18.g1'], 'contains': ['108.p1', '162.m1', '486.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [462, -1, 8643, -1], 'generators': [3469, 5832, 14544, 648, 9300, 11832], 'label': '17496.ro.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '54.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833841
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['324.g1', '324.s1', '324.bc1', '324.cd1'], 'contains': ['1944.bq1', '2916.e1', '2916.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [2729, -1, 8119, -1], 'generators': [9300, 7136, 5928], 'label': '17496.ro.972.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.z1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833842
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.h1', '324.t1', '324.bd1', '324.ce1'], 'contains': ['1944.br1', '2916.e1', '2916.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1045, -1, 7793, -1], 'generators': [9300, 7136, 6720], 'label': '17496.ro.972.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.ba1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833843
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.i1', '324.u1', '324.be1', '324.cf1'], 'contains': ['1944.bs1', '2916.e1', '2916.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1734, -1, 5258, -1], 'generators': [9300, 7136, 5208], 'label': '17496.ro.972.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.bb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833844
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.j1', '324.n1', '324.ba1', '324.bb1', '324.cg1', '324.ch1', '324.ci1'], 'contains': ['1944.bt1', '2916.f1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3108, -1, 7294, -1], 'generators': [9300, 6488, 9936], 'label': '17496.ro.972.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.bc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833848
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.j1', '324.r1', '324.v1', '324.bb1', '324.cj1', '324.ck1', '324.cl1'], 'contains': ['1944.by1', '2916.g1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4345, -1, 7217, -1], 'generators': [9300, 5840, 9936], 'label': '17496.ro.972.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.bg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833849
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.j1', '324.r1', '324.w1', '324.ba1', '324.cj1', '324.ck1', '324.cl1'], 'contains': ['1944.bz1', '2916.g1', '2916.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4370, -1, 7179, -1], 'generators': [9300, 11672, 9936], 'label': '17496.ro.972.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.bh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833850
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['324.k1', '324.s1', '324.x1', '324.bc1', '324.cj1'], 'contains': ['1944.cc1', '2916.g1', '2916.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': [4269, -1, 7831, -1], 'generators': [9300, 5840, 5928], 'label': '17496.ro.972.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.bi1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833851
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '18.h1'], 'contains': ['108.q1', '162.i1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [62, -1, 9243, -1], 'generators': [6, 12312, 5832, 12, 12264, 7344], 'label': '17496.ro.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '54.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833852
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['324.l1', '324.t1', '324.y1', '324.bd1', '324.ck1'], 'contains': ['1944.cd1', '2916.g1', '2916.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1586, -1, 7508, -1], 'generators': [9300, 5840, 6720], 'label': '17496.ro.972.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '972.bj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833853
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['324.m1', '324.u1', '324.z1', '324.be1', '324.cl1'], 'contains': ['1944.ce1', '2916.g1', '2916.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [4432, -1, 5144, -1], 'generators': [9300, 5840, 5208], 'label': '17496.ro.972.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '972.bk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833854
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bf1', '324.bm1', '324.bt1', '324.bz1', '324.cd1', '324.cg1', '324.cj1'], 'contains': ['1944.co1', '2916.h1', '2916.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3134, -1, 7698, -1], 'generators': [9300, 14712, 3240], 'label': '17496.ro.972.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '972.bl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bl1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157833855
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bg1', '324.bn1', '324.bu1', '324.ca1', '324.ce1', '324.ch1', '324.ck1', '486.m1'], 'contains': ['1944.cp1', '2916.h1', '2916.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1873, -1, 7723, -1], 'generators': [5484, 14712, 2016], 'label': '17496.ro.972.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '972.bm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bm1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833856
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '972.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bh1', '324.bo1', '324.bv1', '324.cb1', '324.cf1', '324.ci1', '324.cl1', '486.n1'], 'contains': ['1944.cq1', '2916.h1', '2916.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2879, -1, 5328, -1], 'generators': [9300, 14712, 7200], 'label': '17496.ro.972.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '972.bn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bn1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833857
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.f1', '486.a1', '486.d1', '729.a1'], 'contains': ['2916.a1', '4374.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [413, -1, 9675, -1], 'generators': [3469, 12312, 9300], 'label': '17496.ro.1458.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1458.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833858
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.e1', '162.g1', '162.i1', '486.b1', '486.e1', '729.a1'], 'contains': ['2916.a1', '4374.b1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [129, -1, 9875, -1], 'generators': [6, 12312, 12], 'label': '17496.ro.1458.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1458.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833859
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.d1', '162.h1', '162.j1', '486.c1', '486.f1', '486.g1', '729.a1'], 'contains': ['2916.a1', '4374.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [247, -1, 9541, -1], 'generators': [4255, 12312, 17292], 'label': '17496.ro.1458.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833860
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.m1', '486.a1', '486.h1', '729.b1'], 'contains': ['2916.b1', '4374.a1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [520, -1, 9469, -1], 'generators': [3469, 5832, 9300], 'label': '17496.ro.1458.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1458.d1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833861
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.l1', '486.b1', '486.i1', '486.k1', '729.b1'], 'contains': ['2916.b1', '4374.b1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [341, -1, 9494, -1], 'generators': [6, 12, 5832], 'label': '17496.ro.1458.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1458.e1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833862
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '18.i1'], 'contains': ['108.r1', '162.j1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [275, -1, 8513, -1], 'generators': [12691, 12312, 5832, 8196, 14568, 7200], 'label': '17496.ro.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.i1', 'old_label': '54.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833863
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.k1', '486.c1', '486.j1', '729.b1'], 'contains': ['2916.b1', '4374.c1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 243, 'diagramx': [368, -1, 9443, -1], 'generators': [4255, 17292, 5832], 'label': '17496.ro.1458.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1458.f1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833864
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.d1', '486.h1', '486.l1', '729.c1'], 'contains': ['2916.c1', '4374.a1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [565, -1, 9392, -1], 'generators': [3469, 9300, 12320], 'label': '17496.ro.1458.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1458.g1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833865
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.o1', '486.e1', '486.i1', '729.c1'], 'contains': ['2916.c1', '4374.b1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 243, 'diagramx': [436, -1, 9418, -1], 'generators': [6, 12320, 12], 'label': '17496.ro.1458.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1458.h1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833866
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.n1', '486.f1', '486.j1', '729.c1'], 'contains': ['2916.c1', '4374.c1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 243, 'diagramx': [473, -1, 9367, -1], 'generators': [4255, 17292, 12320], 'label': '17496.ro.1458.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1458.i1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157833867
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.p1', '486.a1', '486.l1'], 'contains': ['2916.d1', '4374.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [2344, -1, 9061, -1], 'generators': [3469, 648, 9300], 'label': '17496.ro.1458.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1458.j1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833868
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.q1', '486.e1', '486.k1'], 'contains': ['2916.e1', '4374.b1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [492, -1, 9341, -1], 'generators': [6, 7136, 12], 'label': '17496.ro.1458.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.e1', 'old_label': '1458.k1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833869
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1458.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.r1', '486.g1', '486.j1'], 'contains': ['2916.f1', '4374.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [546, -1, 9297, -1], 'generators': [4255, 17292, 656], 'label': '17496.ro.1458.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.g1', 'old_label': '1458.l1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833870
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.b1', '648.c1', '648.d1', '648.e1', '648.f1', '648.g1', '648.h1', '648.i1', '972.a1'], 'contains': ['5832.a1', '5832.b1', '5832.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2461, 7450, 4599, 8848], 'generators': [648, 5832], 'label': '17496.ro.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['216.a1', '648.a1'], 'normal_contains': ['5832.a1', '5832.b1'], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '972.883', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833871
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.j1', '648.k1', '648.l1', '648.m1', '972.b1'], 'contains': ['5832.a1', '5832.c1', '5832.e1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2445, 8799, 4966, 9677], 'generators': [12320, 12312], 'label': '17496.ro.1944.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.b1', 'normal_contained_in': ['648.a1'], 'normal_contains': ['5832.a1', '5832.c1'], 'normalizer': '1.a1', 'old_label': '1944.b1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '972.776', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833872
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.bk1', '648.bl1', '648.bm1', '648.bn1', '972.d1'], 'contains': ['5832.b1', '5832.c1', '5832.f1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2476, 6102, 4804, 8018], 'generators': [12320, 5832], 'label': '17496.ro.1944.c1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.c1', 'normal_contained_in': ['648.a1'], 'normal_contains': ['5832.b1', '5832.c1'], 'normalizer': '1.a1', 'old_label': '1944.c1', 'projective_image': '17496.ro', 'quotient_action_image': '4.2', 'quotient_action_kernel': '486.249', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '1944.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833873
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1'], 'contains': ['108.t1', '162.d1', '162.n1', '486.f1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [647, -1, 9070, -1], 'generators': [11623, 7344, 672, 12312, 10620, 12320], 'label': '17496.ro.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '54.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833874
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.n1', '648.o1', '648.p1', '648.q1', '972.c1'], 'contains': ['5832.a1', '5832.f1', '5832.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2715, -1, 4781, -1], 'generators': [656, 12312], 'label': '17496.ro.1944.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '1944.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833875
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '648.j1', '648.n1', '648.r1', '648.s1', '648.t1', '648.u1', '648.v1', '648.w1', '972.h1'], 'contains': ['5832.a1', '5832.h1', '5832.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4336, -1, 4191, -1], 'generators': [3048, 12312], 'label': '17496.ro.1944.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833876
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.c1', '648.j1', '648.n1', '648.r1', '648.s1', '648.t1', '648.x1', '648.y1', '648.z1'], 'contains': ['5832.a1', '5832.j1', '5832.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4828, -1, 4052, -1], 'generators': [9512, 12312], 'label': '17496.ro.1944.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833877
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.d1', '648.k1', '648.o1', '648.u1', '648.x1', '648.ba1', '648.bb1', '648.bc1', '648.bd1', '972.i1'], 'contains': ['5832.a1', '5832.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2902, -1, 6422, -1], 'generators': [14760, 12312], 'label': '17496.ro.1944.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '1944.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833878
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.e1', '648.l1', '648.p1', '648.v1', '648.y1', '648.bc1', '648.be1', '648.bf1', '648.bg1', '972.j1'], 'contains': ['5832.a1', '5832.m1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [288, -1, 4943, -1], 'generators': [6648, 12312], 'label': '17496.ro.1944.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '1944.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833879
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.f1', '648.m1', '648.q1', '648.w1', '648.z1', '648.bc1', '648.bh1', '648.bi1', '648.bj1', '972.k1'], 'contains': ['5832.a1', '5832.n1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1598, -1, 4391, -1], 'generators': [3912, 12312], 'label': '17496.ro.1944.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '1944.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833880
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.g1', '648.k1', '648.o1', '648.r1', '648.x1', '648.ba1', '648.bb1', '648.be1', '648.bh1'], 'contains': ['5832.a1', '5832.o1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3175, -1, 5778, -1], 'generators': [6680, 12312], 'label': '17496.ro.1944.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '1944.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.j1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833881
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.h1', '648.l1', '648.p1', '648.s1', '648.y1', '648.ba1', '648.bf1', '648.bh1'], 'contains': ['5832.a1', '5832.p1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1215, -1, 4712, -1], 'generators': [12152, 12312], 'label': '17496.ro.1944.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '1944.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.k1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833882
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.i1', '648.m1', '648.q1', '648.t1', '648.z1', '648.ba1', '648.be1', '648.bi1'], 'contains': ['5832.a1', '5832.q1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2620, -1, 4314, -1], 'generators': [3920, 12312], 'label': '17496.ro.1944.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '1944.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.l1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833883
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.bo1', '648.bp1', '648.bq1', '648.br1', '972.e1'], 'contains': ['5832.b1', '5832.e1', '5832.g1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2814, -1, 4758, -1], 'generators': [12968, 5832], 'label': '17496.ro.1944.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '1944.m1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833884
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1'], 'contains': ['108.u1', '162.e1', '162.o1', '162.q1', '486.e1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [857, -1, 8834, -1], 'generators': [6, 10584, 8016, 12320, 12312, 12], 'label': '17496.ro.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '54.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833885
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '648.bk1', '648.bo1', '648.bs1', '648.bt1', '648.bu1', '648.bv1', '648.bw1', '648.bx1', '972.l1'], 'contains': ['5832.b1', '5832.h1', '5832.i1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4351, -1, 4168, -1], 'generators': [10584, 5832], 'label': '17496.ro.1944.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833886
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.c1', '648.bk1', '648.bo1', '648.bs1', '648.bt1', '648.bu1', '648.by1', '648.bz1', '648.ca1'], 'contains': ['5832.b1', '5832.j1', '5832.k1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [4813, -1, 4029, -1], 'generators': [9512, 5832], 'label': '17496.ro.1944.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.o1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833887
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.d1', '648.bl1', '648.bp1', '648.bv1', '648.by1', '648.cb1', '648.cc1', '648.cd1', '648.ce1', '648.cf1', '648.cg1', '972.m1'], 'contains': ['5832.b1', '5832.l1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [3666, -1, 6388, -1], 'generators': [2448, 5832], 'label': '17496.ro.1944.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '1944.p1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833888
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.e1', '648.bm1', '648.bq1', '648.bw1', '648.bz1', '648.ce1', '648.ch1', '648.ci1', '648.cj1', '972.n1'], 'contains': ['5832.b1', '5832.m1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1099, -1, 4668, -1], 'generators': [11832, 5832], 'label': '17496.ro.1944.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '1944.q1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833889
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.f1', '648.bn1', '648.br1', '648.bx1', '648.ca1', '648.cf1', '648.cj1', '648.ck1', '648.cl1', '972.o1'], 'contains': ['5832.b1', '5832.n1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2491, -1, 4367, -1], 'generators': [5208, 5832], 'label': '17496.ro.1944.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '1944.r1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833890
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.g1', '648.bl1', '648.bp1', '648.bs1', '648.by1', '648.cb1', '648.cc1', '648.cd1', '648.ch1', '648.ck1'], 'contains': ['5832.b1', '5832.o1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [3706, -1, 5726, -1], 'generators': [6680, 5832], 'label': '17496.ro.1944.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '1944.s1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.s1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833891
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.h1', '648.bm1', '648.bq1', '648.bt1', '648.bz1', '648.cb1', '648.ch1', '648.ci1', '648.cl1'], 'contains': ['5832.b1', '5832.p1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [1569, -1, 4622, -1], 'generators': [12152, 5832], 'label': '17496.ro.1944.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '1944.t1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.t1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833892
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.i1', '648.bn1', '648.br1', '648.bu1', '648.ca1', '648.cc1', '648.ci1', '648.ck1', '648.cl1'], 'contains': ['5832.b1', '5832.q1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [2932, -1, 4344, -1], 'generators': [3920, 5832], 'label': '17496.ro.1944.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '1944.u1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.u1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833893
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.cm1', '648.cn1', '648.co1', '648.cp1', '648.cq1', '648.cr1', '972.f1'], 'contains': ['5832.c1', '5832.d1', '5832.g1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6800, -1, 3153, -1], 'generators': [12320, 648], 'label': '17496.ro.1944.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '1944.v1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833894
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.j1', '648.bk1', '648.cm1', '648.cn1', '648.cs1', '648.ct1', '648.cu1', '648.cv1', '648.cw1', '648.cx1', '972.p1'], 'contains': ['5832.c1', '5832.h1', '5832.k1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [5205, -1, 4098, -1], 'generators': [12320, 10584], 'label': '17496.ro.1944.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.w1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833895
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.d1', '27.b1'], 'contains': ['108.w1', '162.f1', '486.d1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1229, -1, 9668, -1], 'generators': [3469, 12312, 4392, 9300, 12320, 7008], 'label': '17496.ro.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833896
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.j1', '648.bk1', '648.cm1', '648.co1', '648.cs1', '648.ct1', '648.cu1', '648.cy1', '648.cz1', '648.da1'], 'contains': ['5832.c1', '5832.i1', '5832.j1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [4485, -1, 3960, -1], 'generators': [12320, 16416], 'label': '17496.ro.1944.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.x1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833897
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.k1', '648.bl1', '648.cp1', '648.cs1', '648.cv1', '648.cy1', '972.q1'], 'contains': ['5832.c1', '5832.l1', '5832.o1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [5174, -1, 5270, -1], 'generators': [12320, 7224], 'label': '17496.ro.1944.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.y1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833898
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.l1', '648.bm1', '648.cq1', '648.ct1', '648.cw1', '648.cz1', '972.r1'], 'contains': ['5832.c1', '5832.m1', '5832.p1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [1517, -1, 4576, -1], 'generators': [12320, 11832], 'label': '17496.ro.1944.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '1944.z1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833899
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.m1', '648.bn1', '648.cr1', '648.cu1', '648.cx1', '648.da1', '972.s1'], 'contains': ['5832.c1', '5832.n1', '5832.q1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [2852, -1, 3498, -1], 'generators': [12320, 11040], 'label': '17496.ro.1944.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '1944.ba1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833900
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.db1', '648.dc1', '648.dd1', '648.de1', '648.df1', '648.dg1', '972.g1'], 'contains': ['5832.d1', '5832.e1', '5832.f1', '5832.g1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5424, -1, 3439, -1], 'generators': [656, 648], 'label': '17496.ro.1944.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '1944.bb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833901
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '648.cm1', '648.db1', '648.dh1', '648.di1', '648.dj1', '648.dk1', '648.dl1', '648.dm1', '648.dn1', '648.do1', '648.dp1', '648.ec1', '648.ed1', '648.ee1', '972.t1'], 'contains': ['5832.d1', '5832.h1', '5832.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7032, -1, 2630, -1], 'generators': [4104, 6480], 'label': '17496.ro.1944.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833902
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '648.cn1', '648.dc1', '648.dq1', '648.dr1', '648.ds1', '648.dt1', '648.du1', '648.dv1', '648.dw1', '648.dx1', '648.dy1', '648.dz1', '648.ea1', '648.eb1', '648.ec1', '648.ed1', '648.ee1', '648.ef1', '972.u1'], 'contains': ['5832.d1', '5832.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8196, -1, 2606, -1], 'generators': [9936, 648], 'label': '17496.ro.1944.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '1944.bd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833903
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '648.co1', '648.dd1', '648.dn1', '648.do1', '648.dp1', '648.dq1', '648.eg1', '648.eh1', '648.ei1', '648.ej1', '648.ej2', '648.ek1', '648.el1', '648.em1', '648.en1', '648.eo1', '648.ep1'], 'contains': ['5832.d1', '5832.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7499, -1, 1889, -1], 'generators': [3048, 648], 'label': '17496.ro.1944.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '1944.be1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.be1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833904
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.c1', '648.cm1', '648.db1', '648.dr1', '648.ds1', '648.dt1', '648.eg1', '648.eh1', '648.ei1', '648.eq1', '648.er1', '648.es1', '648.fa1', '648.fb1', '648.fc1'], 'contains': ['5832.d1', '5832.j1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7514, -1, 2470, -1], 'generators': [9512, 6480], 'label': '17496.ro.1944.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833905
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.c1', '648.co1', '648.dc1', '648.dd1', '648.dh1', '648.di1', '648.dj1', '648.du1', '648.ej1', '648.ej2', '648.et1', '648.eu1', '648.ev1', '648.ew1', '648.ex1', '648.ey1', '648.ez1', '648.fa1', '648.fb1', '648.fc1'], 'contains': ['5832.d1', '5832.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [7926, -1, 2150, -1], 'generators': [15344, 648], 'label': '17496.ro.1944.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '1944.bg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bg1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833906
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '54.b1', '54.e1', '54.h1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [702, 7220, 8973, 4469], 'generators': [6, 9288, 2592, 12, 1368, 5832, 6480, 2472], 'label': '17496.ro.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '1944.3559'}
  • id: 157833907
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.e1', '27.b1'], 'contains': ['108.w1', '162.g1', '486.e1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [1041, -1, 9731, -1], 'generators': [6, 12312, 504, 12320, 12, 17304], 'label': '17496.ro.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157833908
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.c1', '648.cn1', '648.dd1', '648.dk1', '648.dl1', '648.dm1', '648.dv1', '648.ej1', '648.ej2', '648.eq1', '648.er1', '648.es1', '648.fd1', '648.fe1', '648.ff1', '648.fg1', '648.fh1', '648.fi1', '648.fj1'], 'contains': ['5832.d1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8392, -1, 2173, -1], 'generators': [9512, 648], 'label': '17496.ro.1944.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '1944.bh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833909
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.d1', '648.cp1', '648.de1', '648.dn1', '648.dw1', '648.dx1', '648.dy1', '648.ec1', '648.ek1', '648.el1', '648.em1', '648.eq1', '648.et1', '648.eu1', '648.ev1', '648.fa1', '648.fd1', '648.fe1', '648.ff1', '972.v1'], 'contains': ['5832.d1', '5832.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8111, -1, 2447, -1], 'generators': [3096, 648], 'label': '17496.ro.1944.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bi1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833910
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.e1', '648.cq1', '648.df1', '648.do1', '648.dw1', '648.dx1', '648.ed1', '648.ek1', '648.el1', '648.er1', '648.ew1', '648.ex1', '648.fb1', '648.fg1', '648.fh1', '972.w1'], 'contains': ['5832.d1', '5832.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5684, -1, 2515, -1], 'generators': [816, 6480], 'label': '17496.ro.1944.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833911
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.f1', '648.cr1', '648.dg1', '648.dp1', '648.dw1', '648.dy1', '648.ee1', '648.ek1', '648.em1', '648.es1', '648.ey1', '648.ez1', '648.fc1', '648.fi1', '648.fj1', '972.x1'], 'contains': ['5832.d1', '5832.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7431, -1, 2333, -1], 'generators': [7200, 648], 'label': '17496.ro.1944.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bk1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833912
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.g1', '648.cp1', '648.de1', '648.dh1', '648.dk1', '648.dr1', '648.dz1', '648.ea1', '648.eb1', '648.eg1', '648.en1', '648.eo1', '648.ep1', '648.eq1', '648.et1', '648.eu1', '648.ew1', '648.ex1', '648.ey1', '648.ez1', '648.fa1', '648.fd1', '648.fe1', '648.fg1', '648.fh1', '648.fi1', '648.fj1'], 'contains': ['5832.d1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8484, -1, 2044, -1], 'generators': [6680, 6480], 'label': '17496.ro.1944.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bl1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833913
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.h1', '648.cq1', '648.df1', '648.di1', '648.dl1', '648.ds1', '648.dz1', '648.ea1', '648.eh1', '648.en1', '648.eo1', '648.er1', '648.et1', '648.ev1', '648.ey1', '648.fb1', '648.fd1', '648.ff1', '648.fi1'], 'contains': ['5832.d1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7381, -1, 2218, -1], 'generators': [12152, 6480], 'label': '17496.ro.1944.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833914
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.i1', '648.cr1', '648.dg1', '648.dj1', '648.dm1', '648.dt1', '648.dz1', '648.eb1', '648.ei1', '648.en1', '648.ep1', '648.es1', '648.eu1', '648.ev1', '648.ew1', '648.fc1', '648.fe1', '648.ff1', '648.fg1'], 'contains': ['5832.d1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7844, -1, 2084, -1], 'generators': [3920, 6480], 'label': '17496.ro.1944.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bn1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157833915
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.j1', '648.bo1', '648.db1', '648.dc1', '648.fk1', '648.fl1', '648.fm1', '648.fn1', '648.fo1', '648.fp1', '972.y1'], 'contains': ['5832.e1', '5832.h1', '5832.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4911, -1, 4122, -1], 'generators': [7136, 10584], 'label': '17496.ro.1944.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bo1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833916
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.j1', '648.bo1', '648.db1', '648.dd1', '648.fk1', '648.fl1', '648.fm1', '648.fq1', '648.fr1', '648.fs1'], 'contains': ['5832.e1', '5832.i1', '5832.j1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4873, -1, 3821, -1], 'generators': [7136, 3696], 'label': '17496.ro.1944.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833917
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.k1', '648.bp1', '648.de1', '648.fk1', '648.fn1', '648.fq1', '972.z1'], 'contains': ['5832.e1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5159, -1, 5012, -1], 'generators': [7136, 7224], 'label': '17496.ro.1944.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.bq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833918
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.f1', '27.b1'], 'contains': ['108.w1', '162.h1', '486.f1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [1098, -1, 9602, -1], 'generators': [4255, 12312, 14472, 17292, 12320, 11088], 'label': '17496.ro.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157833919
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.l1', '648.bq1', '648.df1', '648.fl1', '648.fo1', '648.fr1', '972.ba1'], 'contains': ['5832.e1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1554, -1, 4553, -1], 'generators': [7136, 11832], 'label': '17496.ro.1944.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '1944.br1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833920
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.m1', '648.br1', '648.dg1', '648.fm1', '648.fp1', '648.fs1', '972.bb1'], 'contains': ['5832.e1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3620, -1, 3474, -1], 'generators': [8, 11040], 'label': '17496.ro.1944.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '1944.bs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833921
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bk1', '648.db1', '648.dc1', '648.ft1', '648.fu1', '648.fv1', '648.fw1', '648.fx1', '648.fy1', '972.bc1'], 'contains': ['5832.f1', '5832.h1', '5832.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5047, -1, 4075, -1], 'generators': [6488, 10584], 'label': '17496.ro.1944.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bt1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833922
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bk1', '648.db1', '648.dd1', '648.ft1', '648.fu1', '648.fv1', '648.fz1', '648.ga1', '648.gb1'], 'contains': ['5832.f1', '5832.i1', '5832.j1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4858, -1, 3775, -1], 'generators': [656, 16416], 'label': '17496.ro.1944.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.bu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833923
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.o1', '648.bl1', '648.de1', '648.ft1', '648.fw1', '648.fz1', '972.bd1'], 'contains': ['5832.f1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5189, -1, 4989, -1], 'generators': [6488, 7224], 'label': '17496.ro.1944.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.bv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833924
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.p1', '648.bm1', '648.df1', '648.fu1', '648.fx1', '648.ga1', '972.be1'], 'contains': ['5832.f1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1502, -1, 4460, -1], 'generators': [6488, 11832], 'label': '17496.ro.1944.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '1944.bw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833925
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.q1', '648.bn1', '648.dg1', '648.fv1', '648.fy1', '648.gb1', '972.bf1'], 'contains': ['5832.f1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3635, -1, 3413, -1], 'generators': [656, 11040], 'label': '17496.ro.1944.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '1944.bx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833926
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bo1', '648.cm1', '648.dc1', '648.gf1', '648.gg1', '648.gh1', '648.gi1', '648.gj1', '648.gk1', '972.bg1'], 'contains': ['5832.g1', '5832.h1', '5832.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5408, -1, 4006, -1], 'generators': [5840, 10584], 'label': '17496.ro.1944.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.by1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.by1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833927
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bo1', '648.cn1', '648.db1', '648.gc1', '648.gd1', '648.ge1', '648.gi1', '648.gj1', '648.gk1', '972.bh1'], 'contains': ['5832.g1', '5832.h1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5900, -1, 3983, -1], 'generators': [11672, 10584], 'label': '17496.ro.1944.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '1944.bz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833928
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bo1', '648.cm1', '648.dd1', '648.gc1', '648.gd1', '648.ge1', '648.gl1', '648.gm1', '648.gn1'], 'contains': ['5832.g1', '5832.i1', '5832.j1', '5832.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5669, -1, 3682, -1], 'generators': [5840, 3696], 'label': '17496.ro.1944.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.ca1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833929
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1'], 'contains': ['108.x1', '162.i1', '486.e1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [105, -1, 9307, -1], 'generators': [6, 12312, 13176, 12320, 12, 12264], 'label': '17496.ro.54.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '54.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157833930
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.n1', '648.bo1', '648.co1', '648.db1', '648.gf1', '648.gg1', '648.gh1', '648.gl1', '648.gm1', '648.gn1'], 'contains': ['5832.g1', '5832.i1', '5832.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5142, -1, 3752, -1], 'generators': [11672, 16416], 'label': '17496.ro.1944.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '1944.cb1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833931
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['648.o1', '648.bp1', '648.cp1', '648.de1', '648.gc1', '648.gf1', '648.gi1', '648.gl1', '972.bi1'], 'contains': ['5832.g1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6784, -1, 4735, -1], 'generators': [5840, 7224], 'label': '17496.ro.1944.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.cc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833932
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.p1', '648.bq1', '648.cq1', '648.df1', '648.gd1', '648.gg1', '648.gj1', '648.gm1', '972.bj1'], 'contains': ['5832.g1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2605, -1, 4145, -1], 'generators': [5840, 11832], 'label': '17496.ro.1944.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '1944.cd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833933
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.q1', '648.br1', '648.cr1', '648.dg1', '648.ge1', '648.gh1', '648.gk1', '648.gn1', '972.bk1'], 'contains': ['5832.g1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4769, -1, 3384, -1], 'generators': [1304, 11040], 'label': '17496.ro.1944.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '1944.ce1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833934
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.u1', '648.bv1', '648.cs1', '648.dn1', '648.ec1', '648.fk1', '648.ft1', '648.gc1', '648.gf1'], 'contains': ['5832.h1', '5832.i1', '5832.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6647, -1, 4529, -1], 'generators': [3048, 15624], 'label': '17496.ro.1944.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.cf1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833935
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.v1', '648.bw1', '648.ct1', '648.do1', '648.ed1', '648.fl1', '648.fu1', '648.gd1', '648.gg1'], 'contains': ['5832.h1', '5832.i1', '5832.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3598, -1, 3867, -1], 'generators': [15360, 2664], 'label': '17496.ro.1944.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833936
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.w1', '648.bx1', '648.cu1', '648.dp1', '648.ee1', '648.fm1', '648.fv1', '648.ge1', '648.gh1'], 'contains': ['5832.h1', '5832.i1', '5832.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4672, -1, 3315, -1], 'generators': [1104, 10584], 'label': '17496.ro.1944.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.ch1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833937
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.r1', '648.bs1', '648.cs1', '648.dh1', '648.dr1', '648.fk1', '648.fn1', '648.ft1', '648.fw1', '648.gc1', '648.gf1', '648.gi1'], 'contains': ['5832.h1', '5832.j1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6676, -1, 4483, -1], 'generators': [14408, 5136], 'label': '17496.ro.1944.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.ci1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833938
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.s1', '648.bt1', '648.ct1', '648.di1', '648.ds1', '648.fl1', '648.fo1', '648.fu1', '648.fx1', '648.gd1', '648.gg1', '648.gj1'], 'contains': ['5832.h1', '5832.j1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3787, -1, 3890, -1], 'generators': [3680, 5136], 'label': '17496.ro.1944.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cj1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833939
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.t1', '648.bu1', '648.cu1', '648.dj1', '648.dt1', '648.fm1', '648.fp1', '648.fv1', '648.fy1', '648.ge1', '648.gh1', '648.gk1'], 'contains': ['5832.h1', '5832.j1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5127, -1, 3361, -1], 'generators': [3680, 456], 'label': '17496.ro.1944.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.ck1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ck1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833940
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1'], 'contains': ['108.y1', '162.j1', '486.f1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [368, -1, 8447, -1], 'generators': [8371, 12312, 14544, 9204, 12320, 15504], 'label': '17496.ro.54.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.p1', 'old_label': '54.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833941
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.r1', '648.bs1', '648.cv1', '648.dk1', '648.dr1', '648.fk1', '648.ft1', '648.gc1', '648.gi1'], 'contains': ['5832.h1', '5832.k1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [7114, -1, 4437, -1], 'generators': [2744, 5136], 'label': '17496.ro.1944.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.cl1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833942
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.s1', '648.bt1', '648.cw1', '648.dl1', '648.ds1', '648.fl1', '648.fu1', '648.gd1', '648.gj1'], 'contains': ['5832.h1', '5832.k1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4544, -1, 3728, -1], 'generators': [9512, 5136], 'label': '17496.ro.1944.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cm1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833943
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.t1', '648.bu1', '648.cx1', '648.dm1', '648.dt1', '648.fm1', '648.fv1', '648.ge1', '648.gk1'], 'contains': ['5832.h1', '5832.k1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5577, -1, 3338, -1], 'generators': [9512, 456], 'label': '17496.ro.1944.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.cn1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833944
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.u1', '648.bv1', '648.cv1', '648.ec1', '648.fn1', '648.fw1', '648.gi1', '972.bl1'], 'contains': ['5832.h1', '5832.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6108, -1, 4920, -1], 'generators': [14064, 15624], 'label': '17496.ro.1944.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.co1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.co1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833945
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.v1', '648.bw1', '648.cw1', '648.ed1', '648.fo1', '648.fx1', '648.gj1', '972.bm1'], 'contains': ['5832.h1', '5832.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2635, -1, 4214, -1], 'generators': [15360, 2016], 'label': '17496.ro.1944.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1944.cp1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cp1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833946
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.w1', '648.bx1', '648.cx1', '648.ee1', '648.fp1', '648.fy1', '648.gk1', '972.bn1'], 'contains': ['5832.h1', '5832.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4526, -1, 3522, -1], 'generators': [456, 10584], 'label': '17496.ro.1944.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '1944.cq1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cq1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157833947
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['648.r1', '648.bs1', '648.cy1', '648.dh1', '648.eg1', '648.fk1', '648.fq1', '648.ft1', '648.fz1', '648.gf1', '648.gl1'], 'contains': ['5832.i1', '5832.j1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': [6387, -1, 4506, -1], 'generators': [14408, 5784], 'label': '17496.ro.1944.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.cr1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833948
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.s1', '648.bt1', '648.cz1', '648.di1', '648.eh1', '648.fl1', '648.fr1', '648.fu1', '648.ga1', '648.gg1', '648.gm1'], 'contains': ['5832.i1', '5832.j1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [3431, -1, 3659, -1], 'generators': [3680, 5784], 'label': '17496.ro.1944.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cs1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833949
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.t1', '648.bu1', '648.da1', '648.dj1', '648.ei1', '648.fm1', '648.fs1', '648.fv1', '648.gb1', '648.gh1', '648.gn1'], 'contains': ['5832.i1', '5832.j1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [4726, -1, 3176, -1], 'generators': [3680, 1752], 'label': '17496.ro.1944.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.ct1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ct1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833950
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.r1', '648.bs1', '648.cs1', '648.dk1', '648.eg1', '648.fq1', '648.fz1', '648.gc1', '648.gl1'], 'contains': ['5832.i1', '5832.k1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [7047, -1, 4414, -1], 'generators': [2744, 5784], 'label': '17496.ro.1944.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.cu1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833951
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.a1'], 'contains': ['108.ba1', '162.d1', '162.r1', '486.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [605, -1, 9005, -1], 'generators': [11623, 7344, 672, 12312, 10620, 656], 'label': '17496.ro.54.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '54.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833952
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.s1', '648.bt1', '648.ct1', '648.dl1', '648.eh1', '648.fr1', '648.ga1', '648.gd1', '648.gm1'], 'contains': ['5832.i1', '5832.k1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3651, -1, 3636, -1], 'generators': [9512, 5784], 'label': '17496.ro.1944.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cv1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833953
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.t1', '648.bu1', '648.cu1', '648.dm1', '648.ei1', '648.fs1', '648.gb1', '648.ge1', '648.gn1'], 'contains': ['5832.i1', '5832.k1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4695, -1, 3130, -1], 'generators': [9512, 1752], 'label': '17496.ro.1944.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.cw1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833954
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.u1', '648.bv1', '648.cy1', '648.dn1', '648.fq1', '648.fz1', '648.gl1'], 'contains': ['5832.i1', '5832.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6086, -1, 4873, -1], 'generators': [2400, 15624], 'label': '17496.ro.1944.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.cx1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833955
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.v1', '648.bw1', '648.cz1', '648.do1', '648.fr1', '648.ga1', '648.gm1'], 'contains': ['5832.i1', '5832.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2302, -1, 3798, -1], 'generators': [3696, 2664], 'label': '17496.ro.1944.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.cy1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833956
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.w1', '648.bx1', '648.da1', '648.dp1', '648.fs1', '648.gb1', '648.gn1'], 'contains': ['5832.i1', '5832.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3837, -1, 3246, -1], 'generators': [1104, 16416], 'label': '17496.ro.1944.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.cz1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833957
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['648.x1', '648.by1', '648.cs1', '648.eq1', '648.fa1', '648.fk1', '648.fq1', '648.ft1', '648.fz1', '648.gc1', '648.gi1', '648.gl1'], 'contains': ['5832.j1', '5832.k1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': [6754, -1, 4645, -1], 'generators': [4616, 7008], 'label': '17496.ro.1944.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.da1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.da1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833958
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.y1', '648.bz1', '648.ct1', '648.er1', '648.fb1', '648.fl1', '648.fr1', '648.fu1', '648.ga1', '648.gd1', '648.gj1', '648.gm1'], 'contains': ['5832.j1', '5832.k1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [3270, -1, 3705, -1], 'generators': [3032, 12048], 'label': '17496.ro.1944.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.db1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833959
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.z1', '648.ca1', '648.cu1', '648.es1', '648.fc1', '648.fm1', '648.fs1', '648.fv1', '648.gb1', '648.ge1', '648.gk1', '648.gn1'], 'contains': ['5832.j1', '5832.k1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [4950, -1, 3200, -1], 'generators': [2384, 11040], 'label': '17496.ro.1944.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.dc1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833960
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.x1', '648.by1', '648.cy1', '648.fa1', '648.fk1', '648.fw1', '648.fz1', '648.gf1', '648.gl1'], 'contains': ['5832.j1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6405, -1, 4827, -1], 'generators': [5264, 7008], 'label': '17496.ro.1944.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.dd1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833961
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.dd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.x1', '648.by1', '648.cy1', '648.fa1', '648.fn1', '648.fq1', '648.ft1', '648.gf1', '648.gl1'], 'contains': ['5832.j1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [6250, -1, 4850, -1], 'generators': [3968, 7008], 'label': '17496.ro.1944.dd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.dd2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833962
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.f1'], 'contains': ['108.bd1', '162.h1', '486.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1186, -1, 9451, -1], 'generators': [4255, 12312, 16056, 17292, 656, 11400], 'label': '17496.ro.54.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '54.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833983
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '4374.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1458.a1', '1458.d1', '1458.g1', '1458.j1', '2187.a1'], 'contains': ['8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [504, -1, 9395, -1], 'generators': [3469], 'label': '17496.ro.4374.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '4374.a1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4374.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833963
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.y1', '648.bz1', '648.cz1', '648.fb1', '648.fl1', '648.fx1', '648.ga1', '648.gg1', '648.gm1'], 'contains': ['5832.j1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2270, -1, 3913, -1], 'generators': [3680, 12048], 'label': '17496.ro.1944.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.de1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833964
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.de2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.y1', '648.bz1', '648.cz1', '648.fb1', '648.fo1', '648.fr1', '648.fu1', '648.gg1', '648.gm1'], 'contains': ['5832.j1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2287, -1, 3937, -1], 'generators': [2384, 12048], 'label': '17496.ro.1944.de2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.de2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.de2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833965
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.z1', '648.ca1', '648.da1', '648.fc1', '648.fm1', '648.fy1', '648.gb1', '648.gh1', '648.gn1'], 'contains': ['5832.j1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4382, -1, 3269, -1], 'generators': [3032, 11040], 'label': '17496.ro.1944.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.df1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833966
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.df2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.z1', '648.ca1', '648.da1', '648.fc1', '648.fp1', '648.fs1', '648.fv1', '648.gh1', '648.gn1'], 'contains': ['5832.j1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4438, -1, 3292, -1], 'generators': [3680, 11040], 'label': '17496.ro.1944.df2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.df2', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.df2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833967
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.x1', '648.by1', '648.cv1', '648.eq1', '648.fq1', '648.fz1', '648.gc1'], 'contains': ['5832.k1', '5832.l1', '5832.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6769, -1, 4897, -1], 'generators': [11096, 7008], 'label': '17496.ro.1944.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '1944.dg1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833968
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.y1', '648.bz1', '648.cw1', '648.er1', '648.fr1', '648.ga1', '648.gd1'], 'contains': ['5832.k1', '5832.m1', '5832.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1899, -1, 3844, -1], 'generators': [9512, 12048], 'label': '17496.ro.1944.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '1944.dh1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833969
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '1944.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.z1', '648.ca1', '648.cx1', '648.es1', '648.fs1', '648.gb1', '648.ge1'], 'contains': ['5832.k1', '5832.n1', '5832.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4366, -1, 3223, -1], 'generators': [8864, 11040], 'label': '17496.ro.1944.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '1944.di1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.di1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833970
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2187.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['729.a1', '729.b1', '729.c1'], 'contains': ['4374.a1', '4374.b1', '4374.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [404, -1, 9709, -1], 'generators': [3469, 4914], 'label': '17496.ro.2187.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2187.a1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2187.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157833971
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.a1', '972.b1', '972.c1', '972.h1', '972.i1', '972.j1', '972.k1', '1458.a1', '1458.b1', '1458.c1'], 'contains': ['5832.a1', '8748.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1019, -1, 8178, -1], 'generators': [9300, 12312], 'label': '17496.ro.2916.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '2916.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833972
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.a1', '972.d1', '972.e1', '972.l1', '972.m1', '972.n1', '972.o1', '1458.d1', '1458.e1', '1458.f1'], 'contains': ['5832.b1', '8748.a1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [1248, -1, 8052, -1], 'generators': [9300, 5832], 'label': '17496.ro.2916.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '2916.b1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833973
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1'], 'contains': ['108.bf1', '162.j1', '486.g1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [413, -1, 8381, -1], 'generators': [8371, 12312, 14544, 9204, 6488, 15504], 'label': '17496.ro.54.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '54.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833974
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.b1', '972.d1', '972.f1', '972.p1', '972.q1', '972.r1', '972.s1', '1458.g1', '1458.h1', '1458.i1'], 'contains': ['5832.c1', '8748.a1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 81, 'diagramx': [1418, -1, 7950, -1], 'generators': [9300, 12320], 'label': '17496.ro.2916.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '2916.c1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833975
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.a1', '972.f1', '972.g1', '972.t1', '972.u1', '972.v1', '972.w1', '972.x1', '1458.j1'], 'contains': ['5832.d1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [4637, -1, 6356, -1], 'generators': [9300, 648], 'label': '17496.ro.2916.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '2916.d1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833976
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.b1', '972.e1', '972.g1', '972.y1', '972.z1', '972.ba1', '972.bb1', '1458.k1'], 'contains': ['5832.e1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1811, -1, 7796, -1], 'generators': [9300, 16], 'label': '17496.ro.2916.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1', 'old_label': '2916.e1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833977
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.c1', '972.d1', '972.g1', '972.bc1', '972.bd1', '972.be1', '972.bf1', '1458.l1'], 'contains': ['5832.f1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1840, -1, 7775, -1], 'generators': [9300, 656], 'label': '17496.ro.2916.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '2916.f1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833978
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.c1', '972.e1', '972.f1', '972.g1', '972.bg1', '972.bh1', '972.bi1', '972.bj1', '972.bk1'], 'contains': ['5832.g1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [4567, -1, 7314, -1], 'generators': [9300, 12968], 'label': '17496.ro.2916.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '2916.g1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833979
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['972.h1', '972.l1', '972.p1', '972.t1', '972.u1', '972.y1', '972.bc1', '972.bg1', '972.bh1', '972.bl1', '972.bm1', '972.bn1'], 'contains': ['5832.h1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [3132, -1, 7294, -1], 'generators': [9300, 9936], 'label': '17496.ro.2916.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '2916.h1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833980
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['972.i1', '972.m1', '972.q1', '972.v1', '972.z1', '972.bd1', '972.bi1', '972.bl1'], 'contains': ['5832.l1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3054, -1, 7840, -1], 'generators': [9300, 15864], 'label': '17496.ro.2916.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '2916.i1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833981
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['972.j1', '972.n1', '972.r1', '972.w1', '972.ba1', '972.be1', '972.bj1', '972.bm1'], 'contains': ['5832.m1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1075, -1, 7755, -1], 'generators': [9300, 6720], 'label': '17496.ro.2916.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '2916.j1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833982
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '2916.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['972.k1', '972.o1', '972.s1', '972.x1', '972.bb1', '972.bf1', '972.bk1', '972.bn1'], 'contains': ['5832.n1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1872, -1, 4690, -1], 'generators': [9300, 7200], 'label': '17496.ro.2916.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '2916.k1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157833984
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1'], 'contains': ['108.bh1', '162.k1', '162.n1', '162.r1', '486.j1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [683, -1, 8951, -1], 'generators': [2323, 5832, 3312, 8100, 12320, 10896], 'label': '17496.ro.54.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '54.t1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '324.163'}
  • id: 157833985
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '4374.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.n1', '1458.b1', '1458.e1', '1458.h1', '1458.k1', '2187.a1'], 'contains': ['8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [394, -1, 9418, -1], 'generators': [6], 'label': '17496.ro.4374.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '4374.b1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4374.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833986
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '4374.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.m1', '1458.c1', '1458.f1', '1458.i1', '1458.l1', '2187.a1'], 'contains': ['8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [469, -1, 9367, -1], 'generators': [4255], 'label': '17496.ro.4374.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '4374.c1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4374.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833987
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1944.a1', '1944.b1', '1944.d1', '1944.e1', '1944.f1', '1944.g1', '1944.h1', '1944.i1', '1944.j1', '1944.k1', '1944.l1', '2916.a1'], 'contains': ['17496.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2625, 8635, 4712, 9576], 'generators': [12312], 'label': '17496.ro.5832.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '5832.a1', 'normal_contained_in': ['1944.a1', '1944.b1'], 'normal_contains': ['17496.a1'], 'normalizer': '1.a1', 'old_label': '5832.a1', 'projective_image': None, 'quotient_action_image': '1.1', 'quotient_action_kernel': None, 'quotient_action_kernel_order': 5832, 'quotient_fusion': None, 'short_label': '5832.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833988
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1944.a1', '1944.c1', '1944.m1', '1944.n1', '1944.o1', '1944.p1', '1944.q1', '1944.r1', '1944.s1', '1944.t1', '1944.u1', '2916.b1'], 'contains': ['17496.a1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2892, 6267, 4622, 8120], 'generators': [5832], 'label': '17496.ro.5832.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '5832.b1', 'normal_contained_in': ['1944.a1', '1944.c1'], 'normal_contains': ['17496.a1'], 'normalizer': '1.a1', 'old_label': '5832.b1', 'projective_image': '17496.ro', 'quotient_action_image': '2.1', 'quotient_action_kernel': None, 'quotient_action_kernel_order': 2916, 'quotient_fusion': None, 'short_label': '5832.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833989
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1944.b1', '1944.c1', '1944.v1', '1944.w1', '1944.x1', '1944.y1', '1944.z1', '1944.ba1', '2916.c1'], 'contains': ['17496.a1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2940, 7450, 4467, 8848], 'generators': [12320], 'label': '17496.ro.5832.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '5832.c1', 'normal_contained_in': ['1944.b1', '1944.c1'], 'normal_contains': ['17496.a1'], 'normalizer': '1.a1', 'old_label': '5832.c1', 'projective_image': '17496.ro', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2916.ek', 'quotient_action_kernel_order': 2916, 'quotient_fusion': None, 'short_label': '5832.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833990
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.a1', '1944.v1', '1944.bb1', '1944.bc1', '1944.bd1', '1944.be1', '1944.bf1', '1944.bg1', '1944.bh1', '1944.bi1', '1944.bj1', '1944.bk1', '1944.bl1', '1944.bm1', '1944.bn1', '2916.d1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5594, -1, 2470, -1], 'generators': [648], 'label': '17496.ro.5832.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '5832.d1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833991
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.b1', '1944.m1', '1944.bb1', '1944.bo1', '1944.bp1', '1944.bq1', '1944.br1', '1944.bs1', '2916.e1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3829, -1, 4230, -1], 'generators': [8], 'label': '17496.ro.5832.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1944.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '5832.e1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833992
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.c1', '1944.d1', '1944.bb1', '1944.bt1', '1944.bu1', '1944.bv1', '1944.bw1', '1944.bx1', '2916.f1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4192, -1, 4128, -1], 'generators': [656], 'label': '17496.ro.5832.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1944.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '5832.f1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833993
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.d1', '1944.m1', '1944.v1', '1944.bb1', '1944.by1', '1944.bz1', '1944.ca1', '1944.cb1', '1944.cc1', '1944.cd1', '1944.ce1', '2916.g1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5125, -1, 4037, -1], 'generators': [12968], 'label': '17496.ro.5832.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '5832.g1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833994
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.e1', '1944.n1', '1944.w1', '1944.bc1', '1944.bd1', '1944.bo1', '1944.bt1', '1944.by1', '1944.bz1', '1944.cf1', '1944.cg1', '1944.ch1', '1944.ci1', '1944.cj1', '1944.ck1', '1944.cl1', '1944.cm1', '1944.cn1', '1944.co1', '1944.cp1', '1944.cq1', '2916.h1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4947, -1, 3997, -1], 'generators': [15360], 'label': '17496.ro.5832.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '5832.h1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157833995
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1'], 'contains': ['108.bi1', '162.l1', '162.o1', '486.i1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [898, -1, 8771, -1], 'generators': [6, 5832, 13032, 12320, 12, 8304], 'label': '17496.ro.54.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '54.u1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157833996
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.e1', '1944.n1', '1944.x1', '1944.bc1', '1944.be1', '1944.bp1', '1944.bu1', '1944.ca1', '1944.cb1', '1944.cf1', '1944.cg1', '1944.ch1', '1944.cr1', '1944.cs1', '1944.ct1', '1944.cu1', '1944.cv1', '1944.cw1', '1944.cx1', '1944.cy1', '1944.cz1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4658, -1, 3786, -1], 'generators': [16416], 'label': '17496.ro.5832.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '5832.i1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833997
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1944.f1', '1944.o1', '1944.x1', '1944.bf1', '1944.bg1', '1944.bo1', '1944.bp1', '1944.bt1', '1944.bu1', '1944.by1', '1944.ca1', '1944.cb1', '1944.ci1', '1944.cj1', '1944.ck1', '1944.cr1', '1944.cs1', '1944.ct1', '1944.da1', '1944.db1', '1944.dc1', '1944.dd1', '1944.dd2', '1944.de1', '1944.de2', '1944.df1', '1944.df2'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4808, -1, 3902, -1], 'generators': [15344], 'label': '17496.ro.5832.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '5832.j1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833998
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.f1', '1944.o1', '1944.w1', '1944.bf1', '1944.bh1', '1944.bp1', '1944.bu1', '1944.bz1', '1944.ca1', '1944.cl1', '1944.cm1', '1944.cn1', '1944.cu1', '1944.cv1', '1944.cw1', '1944.da1', '1944.db1', '1944.dc1', '1944.dg1', '1944.dh1', '1944.di1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5153, -1, 3814, -1], 'generators': [9512], 'label': '17496.ro.5832.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '5832.k1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157833999
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1944.g1', '1944.p1', '1944.y1', '1944.bi1', '1944.bq1', '1944.bv1', '1944.cc1', '1944.cf1', '1944.co1', '1944.cx1', '1944.da1', '1944.dd1', '1944.dd2', '1944.dg1', '2916.i1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5302, -1, 4885, -1], 'generators': [4920], 'label': '17496.ro.5832.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '5832.l1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157834000
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.h1', '1944.q1', '1944.z1', '1944.bj1', '1944.br1', '1944.bw1', '1944.cd1', '1944.cg1', '1944.cp1', '1944.cy1', '1944.db1', '1944.de1', '1944.de2', '1944.dh1', '2916.j1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2277, -1, 4101, -1], 'generators': [11832], 'label': '17496.ro.5832.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '5832.m1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157834001
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.i1', '1944.r1', '1944.ba1', '1944.bk1', '1944.bs1', '1944.bx1', '1944.ce1', '1944.ch1', '1944.cq1', '1944.cz1', '1944.dc1', '1944.df1', '1944.df2', '1944.di1', '2916.k1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4380, -1, 3402, -1], 'generators': [7200], 'label': '17496.ro.5832.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '5832.n1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157834002
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1944.j1', '1944.s1', '1944.y1', '1944.bl1', '1944.bq1', '1944.bv1', '1944.cc1', '1944.ci1', '1944.cl1', '1944.cr1', '1944.cu1', '1944.da1', '1944.dd1', '1944.dd2', '1944.dg1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5438, -1, 4781, -1], 'generators': [6680], 'label': '17496.ro.5832.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '5832.o1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157834003
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.k1', '1944.t1', '1944.z1', '1944.bm1', '1944.br1', '1944.bw1', '1944.cd1', '1944.cj1', '1944.cm1', '1944.cs1', '1944.cv1', '1944.db1', '1944.de1', '1944.de2', '1944.dh1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2699, -1, 4017, -1], 'generators': [776], 'label': '17496.ro.5832.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.f1', 'old_label': '5832.p1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157834004
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '5832.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.l1', '1944.u1', '1944.ba1', '1944.bn1', '1944.bs1', '1944.bx1', '1944.ce1', '1944.ck1', '1944.cn1', '1944.ct1', '1944.cw1', '1944.dc1', '1944.df1', '1944.df2', '1944.di1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4476, -1, 3350, -1], 'generators': [3920], 'label': '17496.ro.5832.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '5832.q1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157834005
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '8748.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2916.a1', '2916.b1', '2916.c1', '2916.d1', '2916.e1', '2916.f1', '2916.g1', '2916.h1', '2916.i1', '2916.j1', '2916.k1', '4374.a1', '4374.b1', '4374.c1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1495, -1, 7796, -1], 'generators': [9300], 'label': '17496.ro.8748.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '8748.a1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8748.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157834006
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1'], 'contains': ['108.bm1', '162.m1', '486.h1'], 'core': '1944.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [518, -1, 8579, -1], 'generators': [3469, 5832, 14544, 9300, 12320, 11832], 'label': '17496.ro.54.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '54.v1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157834007
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '17496.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5832.a1', '5832.b1', '5832.c1', '5832.d1', '5832.e1', '5832.f1', '5832.g1', '5832.h1', '5832.i1', '5832.j1', '5832.k1', '5832.l1', '5832.m1', '5832.n1', '5832.o1', '5832.p1', '5832.q1', '8748.a1'], 'contains': [], 'core': '17496.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4451, 7450, 4047, 8848], 'generators': [], 'label': '17496.ro.17496.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '17496.a1', 'normal_contained_in': ['5832.a1', '5832.b1', '5832.c1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.a1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157834008
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '54.c1', '54.d1', '54.g1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1258, -1, 8642, -1], 'generators': [3469, 10584, 14256, 9300, 7848, 5832, 648, 14712], 'label': '17496.ro.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157834009
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.b1'], 'contains': ['108.bp1', '162.l1', '162.q1', '486.k1'], 'core': '5832.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [941, -1, 8706, -1], 'generators': [6, 5832, 13032, 12968, 12, 8304], 'label': '17496.ro.54.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '54.w1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157834010
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1'], 'contains': ['108.ca1', '162.p1', '486.l1'], 'core': '5832.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [4171, -1, 6804, -1], 'generators': [3469, 648, 10584, 9300, 12320, 14712], 'label': '17496.ro.54.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '54.x1', 'projective_image': '17496.ro', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157834011
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '36.k2'], 'contains': ['216.a1', '216.c1', '216.bg1', '216.ca1', '216.ch1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2822, 7517, 8269, 6623], 'generators': [12320, 13632, 17352, 5832], 'label': '17496.ro.72.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['216.a1', '648.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157834012
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.b1', '24.c1', '24.d1', '24.e1', '36.a1'], 'contains': ['216.b1', '216.c1', '216.d1', '216.e1', '216.j1', '216.m1', '216.v1', '216.w1', '216.y1', '216.dc1', '216.dj1', '216.dq1', '216.dx1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4744, -1, 3645, -1], 'generators': [12320, 672, 7200, 5832], 'label': '17496.ro.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157834013
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.d1', '24.e1', '36.b1'], 'contains': ['216.b1', '216.c1', '216.d1', '216.k1', '216.n1', '216.t1', '216.x1', '216.dd1', '216.dk1', '216.dr1', '216.dy1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5133, -1, 3705, -1], 'generators': [12320, 10584, 14904, 5832], 'label': '17496.ro.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157834014
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.d1', '24.e1', '36.c1'], 'contains': ['216.b1', '216.c1', '216.e1', '216.l1', '216.o1', '216.u1', '216.z1', '216.de1', '216.dl1', '216.ds1', '216.dz1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5174, -1, 3524, -1], 'generators': [12320, 15360, 17352, 5832], 'label': '17496.ro.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157834015
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '36.d1'], 'contains': ['216.b1', '216.c1', '216.f1', '216.p1', '216.ba1', '216.bw1', '216.cd1', '216.ck1', '216.cr1', '216.cy1', '216.df1', '216.dm1', '216.dt1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5777, -1, 4628, -1], 'generators': [12320, 5832, 15360, 15624, 648], 'label': '17496.ro.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157834016
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.e1', '36.e1'], 'contains': ['216.b1', '216.d1', '216.g1', '216.q1', '216.bb1', '216.bx1', '216.ce1', '216.cl1', '216.cs1', '216.cz1', '216.dg1', '216.dn1', '216.du1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3214, -1, 3801, -1], 'generators': [12320, 5832, 15360, 2664, 648], 'label': '17496.ro.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '72.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157834017
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.e1', '36.f1'], 'contains': ['216.b1', '216.e1', '216.h1', '216.r1', '216.bc1', '216.by1', '216.cf1', '216.cm1', '216.ct1', '216.da1', '216.dh1', '216.do1', '216.dv1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4716, -1, 3271, -1], 'generators': [12320, 5832, 15360, 7200, 648], 'label': '17496.ro.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157834018
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.g1'], 'contains': ['216.b1', '216.i1', '216.s1', '216.db1', '216.di1', '216.dp1', '216.dw1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7582, -1, 2460, -1], 'generators': [12320, 15360, 10584, 5832], 'label': '17496.ro.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157834019
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '54.a1', '54.f1', '54.i1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [936, -1, 8911, -1], 'generators': [4255, 4104, 9072, 17292, 3312, 5832, 648, 8232], 'label': '17496.ro.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '1944.3559'}
  • id: 157834020
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.c1', '24.d1', '36.h1'], 'contains': ['216.c1', '216.d1', '216.e1', '216.bd1', '216.bh1', '216.bm1', '216.br1', '216.bz1', '216.cg1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1759, -1, 5074, -1], 'generators': [12320, 888, 17352, 5832], 'label': '17496.ro.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157834021
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.d1', '36.i1'], 'contains': ['216.c1', '216.d1', '216.be1', '216.bi1', '216.bl1', '216.cn1', '216.cu1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2238, -1, 6174, -1], 'generators': [12320, 888, 7416, 648], 'label': '17496.ro.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157834022
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.d1', '36.j1'], 'contains': ['216.c1', '216.e1', '216.bf1', '216.bj1', '216.bs1', '216.co1', '216.cv1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2880, -1, 5014, -1], 'generators': [12320, 7200, 15120, 648], 'label': '17496.ro.72.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157834023
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '36.k1'], 'contains': ['216.c1', '216.bg2', '216.bk1', '216.cp1', '216.cw1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3521, -1, 8208, -1], 'generators': [12320, 2448, 14904, 648], 'label': '17496.ro.72.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157834024
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.c1', '36.l1'], 'contains': ['216.d1', '216.e1', '216.bn1', '216.bp1', '216.bt1', '216.cq1', '216.cx1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1065, -1, 4762, -1], 'generators': [12320, 888, 7200, 648], 'label': '17496.ro.72.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157834025
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.m1'], 'contains': ['216.d1', '216.bo1', '216.bq1', '216.cb1', '216.ci1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [311, -1, 6113, -1], 'generators': [12320, 13560, 216, 5832], 'label': '17496.ro.72.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157834026
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.n1'], 'contains': ['216.e1', '216.bu1', '216.bv1', '216.cc1', '216.cj1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1683, -1, 4702, -1], 'generators': [12320, 11040, 2880, 5832], 'label': '17496.ro.72.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '72.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157834027
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.b1', '24.g1', '24.h1', '24.i1'], 'contains': ['216.h1', '216.j1', '216.m1', '216.o1', '216.u1', '216.w1', '216.y1', '216.bd1', '216.bf1', '216.bm1', '216.bn1', '216.bs1', '216.bu1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3687, -1, 3964, -1], 'generators': [4976, 11040, 17352], 'label': '17496.ro.72.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157834028
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.c1', '24.f1', '24.h1', '24.i1'], 'contains': ['216.g1', '216.j1', '216.m1', '216.n1', '216.t1', '216.w1', '216.y1', '216.bd1', '216.be1', '216.bl1', '216.bo1', '216.br1', '216.bt1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3709, -1, 4091, -1], 'generators': [7280, 17376, 10584], 'label': '17496.ro.72.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157834029
    {'ambient': '17496.ro', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.d1', '24.f1', '24.g1', '24.i1'], 'contains': ['216.f1', '216.j1', '216.n1', '216.o1', '216.v1', '216.x1', '216.z1', '216.bg1', '216.bg2', '216.bl1', '216.bm1', '216.br1', '216.bs1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3822, -1, 4060, -1], 'generators': [10448, 15360, 15120], 'label': '17496.ro.72.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '81.15'}