Abstract group data - 324.20

Formats: - HTML - YAML - JSON - 2025-11-08T23:09:46.814465

• 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': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [2, 6, 3, 6, 3, 9], 'aut_gens': [[1, 4, 12, 36], [1, 8, 24, 36], [59, 248, 12, 296], [217, 4, 12, 252], [11, 4, 12, 68], [5, 4, 12, 60], [289, 28, 12, 144]], 'aut_group': '5832.of', 'aut_hash': 6219057450053085502, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5832, 'aut_permdeg': 54, 'aut_perms': [70402591850076690367864978755917773215922088907599318633123515801381, 224066297042973371496017943375372601286132044354245037033514090396015432, 2583153301740872671836521938680083285888990022851486172473876960971611, 224723436232129619988535398990449202423671328577798368523861659720585070, 48049601944554360248808400834714385129952267303107142586698804673646496, 214779775831630781913783150444519130339488865635213900822531282409209891], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 6, 3, 1], [4, 27, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 3, 1], [9, 6, 9, 1], [12, 27, 4, 1], [18, 6, 9, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_3^4.S_3^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '2916.fs', 'autcentquo_hash': 5014850949365468175, 'autcentquo_nilpotent': False, 'autcentquo_order': 2916, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^4.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 2, 3], [3, 6, 3], [4, 27, 2], [6, 1, 2], [6, 2, 3], [6, 6, 3], [9, 6, 9], [12, 27, 4], [18, 6, 9]], 'center_label': '6.2', 'center_order': 6, 'central_product': False, 'central_quotient': '54.7', 'commutator_count': 2, 'commutator_label': '81.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 20, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 6, 1, 3], [4, 27, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 1, 3], [9, 6, 3, 3], [12, 27, 4, 1], [18, 6, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3024, 'exponent': 36, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '18.4', 'hash': 20, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 3, 1, 9], 'inner_gens': [[1, 8, 12, 288], [9, 4, 12, 48], [1, 4, 12, 36], [73, 28, 12, 36]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 54, 'inner_split': True, 'inner_tex': 'C_3:D_9', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 26], [3, 8], [6, 4]], 'label': '324.20', 'linC_count': 108, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 7, 'linQ_dim': 12, 'linQ_dim_count': 1, 'linR_count': 18, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C3*C18).S3', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 42, 'number_divisions': 22, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 37, 'number_subgroup_classes': 61, 'number_subgroups': 233, 'old_label': None, 'order': 324, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1], [3, 26], [4, 54], [6, 26], [9, 54], [12, 108], [18, 54]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [3, 3, 2, 2, 6], 'outer_gen_pows': [1, 0, 0, 0, 0], 'outer_gens': [[1, 8, 12, 196], [1, 4, 12, 252], [3, 4, 12, 36], [1, 8, 24, 56], [3, 112, 12, 36]], 'outer_group': '108.28', 'outer_hash': 28, 'outer_nilpotent': False, 'outer_order': 108, 'outer_permdeg': 11, 'outer_perms': [10968600, 4436886, 1, 209929, 8484529], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2:D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [6, 8], [12, 3]], 'representations': {'PC': {'code': 2157241135633182807119, 'gens': [1, 3, 4, 5], 'pres': [6, -2, -2, -3, -3, 3, -3, 12, 146, 8644, 376, 118, 7781]}, 'Perm': {'d': 22, 'gens': [7676448775789333809, 16, 58760988487130045520, 109865802469059237000, 1133733000, 158651951566268160000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_{18}).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: 109782909
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 20, 'group_order': 324, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 109782920
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 20, 'group_order': 324, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2, 'size': 1}
  • id: 109782931
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 20, 'group_order': 324, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 12, 'size': 1}
  • id: 109782942
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 20, 'group_order': 324, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 24, 'size': 1}
  • id: 109782946
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 20, 'group_order': 324, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 216, 'size': 2}
  • id: 109782947
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 20, 'group_order': 324, 'label': '3C1', 'order': 3, 'powers': [7, 1], 'representative': 240, 'size': 2}
  • id: 109782948
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 20, 'group_order': 324, 'label': '3C-1', 'order': 3, 'powers': [6, 1], 'representative': 120, 'size': 2}
  • id: 109782949
    {'aut_label': '3D', 'centralizer': '6.a1.a1', 'counter': 8, 'group_counter': 20, 'group_order': 324, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 8, 'size': 6}
  • id: 109782950
    {'aut_label': '3D', 'centralizer': '6.a1.a1', 'counter': 9, 'group_counter': 20, 'group_order': 324, 'label': '3E', 'order': 3, 'powers': [9, 1], 'representative': 224, 'size': 6}
  • id: 109782910
    {'aut_label': '3D', 'centralizer': '6.a1.a1', 'counter': 10, 'group_counter': 20, 'group_order': 324, 'label': '3F', 'order': 3, 'powers': [10, 1], 'representative': 116, 'size': 6}
  • id: 109782911
    {'aut_label': '4A1', 'centralizer': '27.a1.a1', 'counter': 11, 'group_counter': 20, 'group_order': 324, 'label': '4A1', 'order': 4, 'powers': [2, 12], 'representative': 115, 'size': 27}
  • id: 109782912
    {'aut_label': '4A1', 'centralizer': '27.a1.a1', 'counter': 12, 'group_counter': 20, 'group_order': 324, 'label': '4A-1', 'order': 4, 'powers': [2, 11], 'representative': 113, 'size': 27}
  • id: 109782913
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 20, 'group_order': 324, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 26, 'size': 1}
  • id: 109782914
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 20, 'group_order': 324, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 14, 'size': 1}
  • id: 109782915
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 20, 'group_order': 324, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 110, 'size': 2}
  • id: 109782916
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 16, 'group_counter': 20, 'group_order': 324, 'label': '6C1', 'order': 6, 'powers': [6, 2], 'representative': 122, 'size': 2}
  • id: 109782917
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 17, 'group_counter': 20, 'group_order': 324, 'label': '6C-1', 'order': 6, 'powers': [7, 2], 'representative': 134, 'size': 2}
  • id: 109782918
    {'aut_label': '6D', 'centralizer': '6.a1.a1', 'counter': 18, 'group_counter': 20, 'group_order': 324, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 6, 'size': 6}
  • id: 109782919
    {'aut_label': '6D', 'centralizer': '6.a1.a1', 'counter': 19, 'group_counter': 20, 'group_order': 324, 'label': '6E', 'order': 6, 'powers': [9, 2], 'representative': 114, 'size': 6}
  • id: 109782921
    {'aut_label': '6D', 'centralizer': '6.a1.a1', 'counter': 20, 'group_counter': 20, 'group_order': 324, 'label': '6F', 'order': 6, 'powers': [10, 2], 'representative': 222, 'size': 6}
  • id: 109782922
    {'aut_label': '9A1', 'centralizer': '6.b1.a1', 'counter': 21, 'group_counter': 20, 'group_order': 324, 'label': '9A1', 'order': 9, 'powers': [22, 5], 'representative': 72, 'size': 6}
  • id: 109782923
    {'aut_label': '9A1', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 20, 'group_order': 324, 'label': '9A2', 'order': 9, 'powers': [23, 5], 'representative': 144, 'size': 6}
  • id: 109782924
    {'aut_label': '9A1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 20, 'group_order': 324, 'label': '9A4', 'order': 9, 'powers': [21, 5], 'representative': 288, 'size': 6}
  • id: 109782925
    {'aut_label': '9A1', 'centralizer': '6.b1.b1', 'counter': 24, 'group_counter': 20, 'group_order': 324, 'label': '9B1', 'order': 9, 'powers': [25, 5], 'representative': 92, 'size': 6}
  • id: 109782926
    {'aut_label': '9A1', 'centralizer': '6.b1.b1', 'counter': 25, 'group_counter': 20, 'group_order': 324, 'label': '9B2', 'order': 9, 'powers': [26, 5], 'representative': 148, 'size': 6}
  • id: 109782927
    {'aut_label': '9A1', 'centralizer': '6.b1.b1', 'counter': 26, 'group_counter': 20, 'group_order': 324, 'label': '9B4', 'order': 9, 'powers': [24, 5], 'representative': 308, 'size': 6}
  • id: 109782928
    {'aut_label': '9A1', 'centralizer': '6.b1.c1', 'counter': 27, 'group_counter': 20, 'group_order': 324, 'label': '9C1', 'order': 9, 'powers': [28, 5], 'representative': 176, 'size': 6}
  • id: 109782929
    {'aut_label': '9A1', 'centralizer': '6.b1.c1', 'counter': 28, 'group_counter': 20, 'group_order': 324, 'label': '9C2', 'order': 9, 'powers': [29, 5], 'representative': 292, 'size': 6}
  • id: 109782930
    {'aut_label': '9A1', 'centralizer': '6.b1.c1', 'counter': 29, 'group_counter': 20, 'group_order': 324, 'label': '9C4', 'order': 9, 'powers': [27, 5], 'representative': 284, 'size': 6}
  • id: 109782932
    {'aut_label': '12A1', 'centralizer': '27.a1.a1', 'counter': 30, 'group_counter': 20, 'group_order': 324, 'label': '12A1', 'order': 12, 'powers': [13, 11], 'representative': 125, 'size': 27}
  • id: 109782933
    {'aut_label': '12A1', 'centralizer': '27.a1.a1', 'counter': 31, 'group_counter': 20, 'group_order': 324, 'label': '12A-1', 'order': 12, 'powers': [14, 12], 'representative': 139, 'size': 27}
  • id: 109782934
    {'aut_label': '12A1', 'centralizer': '27.a1.a1', 'counter': 32, 'group_counter': 20, 'group_order': 324, 'label': '12A5', 'order': 12, 'powers': [14, 11], 'representative': 137, 'size': 27}
  • id: 109782935
    {'aut_label': '12A1', 'centralizer': '27.a1.a1', 'counter': 33, 'group_counter': 20, 'group_order': 324, 'label': '12A-5', 'order': 12, 'powers': [13, 12], 'representative': 127, 'size': 27}
  • id: 109782936
    {'aut_label': '18A1', 'centralizer': '6.b1.a1', 'counter': 34, 'group_counter': 20, 'group_order': 324, 'label': '18A1', 'order': 18, 'powers': [21, 15], 'representative': 38, 'size': 6}
  • id: 109782937
    {'aut_label': '18A1', 'centralizer': '6.b1.a1', 'counter': 35, 'group_counter': 20, 'group_order': 324, 'label': '18A5', 'order': 18, 'powers': [23, 15], 'representative': 146, 'size': 6}
  • id: 109782938
    {'aut_label': '18A1', 'centralizer': '6.b1.a1', 'counter': 36, 'group_counter': 20, 'group_order': 324, 'label': '18A7', 'order': 18, 'powers': [22, 15], 'representative': 74, 'size': 6}
  • id: 109782939
    {'aut_label': '18A1', 'centralizer': '6.b1.b1', 'counter': 37, 'group_counter': 20, 'group_order': 324, 'label': '18B1', 'order': 18, 'powers': [24, 15], 'representative': 42, 'size': 6}
  • id: 109782940
    {'aut_label': '18A1', 'centralizer': '6.b1.b1', 'counter': 38, 'group_counter': 20, 'group_order': 324, 'label': '18B5', 'order': 18, 'powers': [26, 15], 'representative': 150, 'size': 6}
  • id: 109782941
    {'aut_label': '18A1', 'centralizer': '6.b1.b1', 'counter': 39, 'group_counter': 20, 'group_order': 324, 'label': '18B7', 'order': 18, 'powers': [25, 15], 'representative': 82, 'size': 6}
  • id: 109782943
    {'aut_label': '18A1', 'centralizer': '6.b1.c1', 'counter': 40, 'group_counter': 20, 'group_order': 324, 'label': '18C1', 'order': 18, 'powers': [27, 15], 'representative': 78, 'size': 6}
  • id: 109782944
    {'aut_label': '18A1', 'centralizer': '6.b1.c1', 'counter': 41, 'group_counter': 20, 'group_order': 324, 'label': '18C5', 'order': 18, 'powers': [29, 15], 'representative': 46, 'size': 6}
  • id: 109782945
    {'aut_label': '18A1', 'centralizer': '6.b1.c1', 'counter': 42, 'group_counter': 20, 'group_order': 324, 'label': '18C7', 'order': 18, 'powers': [28, 15], 'representative': 186, 'size': 6}
• 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: 4399925
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.1a', '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], 'schur_index': 1}
  • id: 4399936
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.1b', '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], 'schur_index': 1}
  • id: 4399940
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 4399941
    {'cdim': 2, 'counter': 4, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, 2, -1], 'schur_index': 1}
  • id: 4399942
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, -1, -1, 2, -1, 2, -1, -1, -1, 2], 'schur_index': 1}
  • id: 4399943
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 4399944
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4399945
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2e', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, 1, -2, 1], 'schur_index': 2}
  • id: 4399946
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2f', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -1, 2, 2, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 1, 1, -2, 1, -2, 1, 1, 1, -2], 'schur_index': 2}
  • id: 4399926
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2g', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 2}
  • id: 4399927
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2h', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 2}
  • id: 4399928
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2i', 'multiplicity': 3, 'nt': [9, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -3, -3, 6, 0, 0, 6, 6, -3, -3, -3, 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], 'schur_index': 1}
  • id: 4399929
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2j', 'multiplicity': 3, 'nt': [9, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -3, 6, -3, 0, 0, 6, 6, -3, -3, -3, -3, -3, 6, 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: 4399930
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2k', 'multiplicity': 3, 'nt': [9, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, 6, -3, -3, 0, 0, 6, 6, -3, -3, -3, -3, 6, -3, 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: 4399931
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2l', 'multiplicity': 3, 'nt': [36, 9], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, -3, -3, 6, 0, 0, -6, -6, 3, 3, 3, -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], 'schur_index': 2}
  • id: 4399932
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2m', 'multiplicity': 3, 'nt': [36, 9], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, -3, 6, -3, 0, 0, -6, -6, 3, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4399933
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.2n', 'multiplicity': 3, 'nt': [36, 9], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, 6, -3, -3, 0, 0, -6, -6, 3, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4399934
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.3a', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, 0, 0, 0, 2, 2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4399935
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.3b', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, 0, 0, 0, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4399937
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.3c', 'multiplicity': 4, 'nt': [36, 78], 'qdim': 12, 'qvalues': [12, -12, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 6, 6, -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], 'schur_index': 1}
  • id: 4399938
    {'cdim': 6, 'counter': 21, 'faithful': False, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.6a', 'multiplicity': 2, 'nt': [18, 87], 'qdim': 12, 'qvalues': [12, 12, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 4399939
    {'cdim': 6, 'counter': 22, 'faithful': True, 'group': '324.20', 'group_order': 324, 'image': None, 'label': '324.20.6b', 'multiplicity': 2, 'nt': [36, 488], 'qdim': 12, 'qvalues': [12, -12, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 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], '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: 6690547
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 324, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 324, 'label': '324.20.1a', '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]]]}
  • id: 6690558
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 324, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 162, 'label': '324.20.1b', '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]]]}
  • id: 6690569
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 324, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 81, 'label': '324.20.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6690580
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 324, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 81, 'label': '324.20.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6690584
    {'center': '6.b1.b1', 'center_index': 6, 'center_order': 54, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.b1', 'kernel_order': 54, 'label': '324.20.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
  • id: 6690585
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 54, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 54, 'label': '324.20.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
  • id: 6690586
    {'center': '6.b1.c1', 'center_index': 6, 'center_order': 54, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.c1', 'kernel_order': 54, 'label': '324.20.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6690587
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 54, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 54, 'label': '324.20.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6690588
    {'center': '6.b1.b1', 'center_index': 6, 'center_order': 54, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.b1', 'kernel_order': 27, 'label': '324.20.2e', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
  • id: 6690548
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 54, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.a1', 'kernel_order': 27, 'label': '324.20.2f', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
  • id: 6690549
    {'center': '6.b1.c1', 'center_index': 6, 'center_order': 54, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.c1', 'kernel_order': 27, 'label': '324.20.2g', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6690550
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 54, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 27, 'label': '324.20.2h', 'nt': [12, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6690551
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 13, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.b1', 'kernel_order': 18, 'label': '324.20.2i1', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
  • id: 6690552
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 14, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.b1', 'kernel_order': 18, 'label': '324.20.2i2', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 6690553
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 15, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.b1', 'kernel_order': 18, 'label': '324.20.2i3', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 6690554
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 16, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.a1', 'kernel_order': 18, 'label': '324.20.2j1', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 6690555
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 17, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.a1', 'kernel_order': 18, 'label': '324.20.2j2', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]]]}
  • id: 6690556
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 18, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.a1', 'kernel_order': 18, 'label': '324.20.2j3', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[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, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 6690557
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 19, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.c1', 'kernel_order': 18, 'label': '324.20.2k1', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]]]}
  • id: 6690559
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 20, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.c1', 'kernel_order': 18, 'label': '324.20.2k2', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6690560
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 21, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.b1.c1', 'kernel_order': 18, 'label': '324.20.2k3', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]]]}
  • id: 6690561
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 22, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.b1', 'kernel_order': 9, 'label': '324.20.2l1', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]]]}
  • id: 6690562
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 23, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.b1', 'kernel_order': 9, 'label': '324.20.2l2', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6690563
    {'center': '18.b1.b1', 'center_index': 18, 'center_order': 18, 'counter': 24, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.b1', 'kernel_order': 9, 'label': '324.20.2l3', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 6690564
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 25, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.a1', 'kernel_order': 9, 'label': '324.20.2m1', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6690565
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 26, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.a1', 'kernel_order': 9, 'label': '324.20.2m2', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]]]}
  • id: 6690566
    {'center': '18.b1.a1', 'center_index': 18, 'center_order': 18, 'counter': 27, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.a1', 'kernel_order': 9, 'label': '324.20.2m3', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[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, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 6690567
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 28, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.c1', 'kernel_order': 9, 'label': '324.20.2n1', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]]]}
  • id: 6690568
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 29, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.c1', 'kernel_order': 9, 'label': '324.20.2n2', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6690570
    {'center': '18.b1.c1', 'center_index': 18, 'center_order': 18, 'counter': 30, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '36.1', 'image_order': 36, 'indicator': -1, 'kernel': '36.b1.c1', 'kernel_order': 9, 'label': '324.20.2n3', 'nt': [36, 9], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 6690571
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 6, 'label': '324.20.3a1', 'nt': [9, 12], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[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]], [[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]]]}
  • id: 6690572
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 32, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 6, 'label': '324.20.3a2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[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]], [[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]]]}
  • id: 6690573
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 33, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 6, 'label': '324.20.3b1', 'nt': [18, 24], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[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]], [[-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]]]}
  • id: 6690574
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 34, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 6, 'label': '324.20.3b2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[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]], [[-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]]]}
  • id: 6690575
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 35, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 3, 'label': '324.20.3c1', 'nt': [36, 78], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[-3, 4]], [[3, 2]], [[-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]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6690576
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 36, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 3, 'label': '324.20.3c2', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[3, 2]], [[-3, 4]], [[-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]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6690577
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 37, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 3, 'label': '324.20.3c3', 'nt': [36, 78], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[-3, 4]], [[3, 2]], [[-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]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6690578
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 18, 'counter': 38, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 3, 'label': '324.20.3c4', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[3, 2]], [[-3, 4]], [[-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]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6690579
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 6, 'counter': 39, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '162.17', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 2, 'label': '324.20.6a1', 'nt': [18, 87], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-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]]]}
  • id: 6690581
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 6, 'counter': 40, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '162.17', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 2, 'label': '324.20.6a2', 'nt': [18, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-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]]]}
  • id: 6690582
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 6, 'counter': 41, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '324.20', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 1, 'label': '324.20.6b1', 'nt': [36, 488], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[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]]]}
  • id: 6690583
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 6, 'counter': 42, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '324.20', 'group_counter': 20, 'group_order': 324, 'image': None, 'image_isoclass': '324.20', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 1, 'label': '324.20.6b2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[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]]]}
• 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: 65470343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '324.20.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.20', 'subgroup_hash': 20, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times C_{18}).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 65470354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 162, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.3.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.3.b1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 81, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '324.20.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 3}
  • id: 65470402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470351
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470352
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470353
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.9.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 65470356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.12.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 18, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.18.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470364
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470367
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.18.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 65470368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470369
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65470370
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470371
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470372
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.27.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470373
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.27.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65470374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 9, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 65470375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 65470377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 65470378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.20.36.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 65470379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 65470380
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470381
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470382
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.36.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 65470383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.20.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 65470384
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 6, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.20.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_9', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470385
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 6, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.20.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470386
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470388
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470389
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.54.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.54.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65470391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '324.20.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 2}
  • id: 65470392
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.20.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_9', 'simple': True, 'solvable': True, 'special_labels': ['D2'], '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: 65470393
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 3, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.20.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_4', 'simple': True, 'solvable': True, 'special_labels': ['C5'], '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: 65470394
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 65470395
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 65470396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 65470397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.20.108.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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: 65470399
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.20.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_9', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 65470400
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.20', 'ambient_counter': 20, 'ambient_order': 324, 'ambient_tex': '(C_3\\times C_{18}).S_3', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '324.20.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '324.20', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_3\\times C_{18}).S_3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C6'], '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: 65470394
    {'ambient': '324.20', 'aut_centralizer_order': 1458, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.e1.a1', '54.c1.a1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2976, -1, 2752, -1, 3877, -1, 4507, -1], 'generators': [120], 'label': '324.20.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470343
    {'ambient': '324.20', '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': '54.a1.a1', 'complements': ['324.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3836, 5136, 4863, 4045, 3859, 4174, 4552, 3385], 'generators': [1, 108, 12, 2, 4, 36], 'label': '324.20.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
  • id: 65470344
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['12.b1.b1', '18.a1.a1', '18.d1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2632, 8478, 1866, 4045, 2246, 4174, 1833, 704], 'generators': [2, 256, 12, 108], 'label': '324.20.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.b1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470345
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['12.b1.c1', '18.a1.a1', '18.d1.c1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2632, 8478, 3348, 736, 2246, 4174, 2644, 3385], 'generators': [2, 184, 12, 108], 'label': '324.20.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.c1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470346
    {'ambient': '324.20', 'aut_centralizer_order': 27, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 243, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.a1.a1', '27.a1.a1', '27.b1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7979, -1, 6910, -1, 6006, -1, 6439, -1], 'generators': [1, 12, 2, 108], 'label': '324.20.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470347
    {'ambient': '324.20', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 243, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.a1', '27.a1.a1', '27.c1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9493, -1, 7670, -1, 8696, -1, 8102, -1], 'generators': [1, 12, 2, 4], 'label': '324.20.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470348
    {'ambient': '324.20', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 243, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.b1', '27.a1.a1', '27.c1.b1'], 'core': '18.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9493, -1, 8967, -1, 8696, -1, 7271, -1], 'generators': [1, 12, 2, 112], 'label': '324.20.9.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '9.b1.b1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470349
    {'ambient': '324.20', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 243, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.c1', '27.a1.a1', '27.c1.c1'], 'core': '18.b1.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [9493, -1, 9731, -1, 8696, -1, 9497, -1], 'generators': [1, 12, 2, 220], 'label': '324.20.9.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.c1', 'old_label': '9.b1.c1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470350
    {'ambient': '324.20', 'aut_centralizer_order': 9, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.102', 'aut_weyl_index': 27, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.c1.a1', '27.b1.a1', '27.c1.a1', '27.c1.b1', '27.c1.c1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6775, -1, 8321, -1, 7274, -1, 8800, -1], 'generators': [1, 2, 4, 108], 'label': '324.20.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '9.c1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 65470351
    {'ambient': '324.20', 'aut_centralizer_order': 6, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.26', 'aut_weyl_index': 54, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.d1.a1', '27.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3629, -1, 4522, -1, 3406, -1, 5010, -1], 'generators': [1, 2, 36, 108], 'label': '324.20.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.d1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470352
    {'ambient': '324.20', 'aut_centralizer_order': 6, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.26', 'aut_weyl_index': 54, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1'], 'contains': ['18.d1.b1', '27.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3629, -1, 4104, -1, 3406, -1, 4094, -1], 'generators': [1, 2, 64, 108], 'label': '324.20.9.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '9.d1.b1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470353
    {'ambient': '324.20', 'aut_centralizer_order': 6, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.26', 'aut_weyl_index': 54, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1'], 'contains': ['18.d1.c1', '27.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3629, -1, 4941, -1, 3406, -1, 4552, -1], 'generators': [1, 2, 88, 108], 'label': '324.20.9.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.c1', 'old_label': '9.d1.c1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470354
    {'ambient': '324.20', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '972.455', 'aut_weyl_index': 6, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2751, 5136, 3126, 4045, 2246, 4174, 2739, 3385], 'generators': [2, 108, 4, 252, 12], 'label': '324.20.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.b1', '6.b1.c1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 65470355
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 162, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1', '36.c1.a1', '36.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2330, 2120, 4076, 6645, 2319, 3559, 3506, 5726], 'generators': [4, 12, 108], 'label': '324.20.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470356
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.a1', 'complements': ['27.c1.a1', '27.c1.b1', '27.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['36.a1.a1', '36.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [507, 6114, 887, 2391, 534, 1250, 1648, 3346], 'generators': [12, 252], 'label': '324.20.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470357
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.b1', 'complements': ['27.c1.a1', '27.c1.b1', '27.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.b1'], 'contains': ['36.a1.a1', '36.d1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [507, 6114, 269, 5152, 534, 1250, 294, 704], 'generators': [256, 12], 'label': '324.20.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.a1.a1', '6.b1.b1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470358
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.c1', 'complements': ['27.c1.a1', '27.c1.b1', '27.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.c1'], 'contains': ['36.a1.a1', '36.d1.c1'], 'core': '12.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [507, 6114, 1506, 3772, 534, 1250, 971, 2025], 'generators': [184, 12], 'label': '324.20.12.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.c1', 'normal_contained_in': ['4.a1.a1', '6.b1.c1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.c1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470359
    {'ambient': '324.20', 'aut_centralizer_order': 1458, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1458, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4531, 7364, 2911, 2421, 3306, 5869, 4049, 4667], 'generators': [2, 12, 108], 'label': '324.20.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.b1', '6.b1.c1', '6.b1.a1'], 'normal_contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '54.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470360
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.a1.a1', '54.d1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 1603, 5186, 6116, 7835, 8750, 5861, 6785], 'generators': [2, 4, 12], 'label': '324.20.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['36.b1.a1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470361
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.b1'], 'contains': ['36.b1.b1', '54.a1.a1', '54.d1.b1'], 'core': '18.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 1603, 7288, 7884, 7835, 8750, 5184, 9427], 'generators': [2, 112, 12], 'label': '324.20.18.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['36.b1.b1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.b1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470362
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.c1'], 'contains': ['36.b1.c1', '54.a1.a1', '54.d1.c1'], 'core': '18.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 1603, 7907, 9264, 7835, 8750, 7216, 8105], 'generators': [2, 220, 12], 'label': '324.20.18.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['36.b1.c1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.c1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470363
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.c1.a1'], 'contains': ['36.c1.a1', '54.b1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3362, -1, 6669, -1, 4538, -1, 6539, -1], 'generators': [2, 4, 108], 'label': '324.20.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470364
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.d1.a1'], 'contains': ['36.d1.a1', '54.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1049, -1, 2001, -1, 1549, -1, 3083, -1], 'generators': [2, 252, 108], 'label': '324.20.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470365
    {'ambient': '324.20', 'aut_centralizer_order': 9, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.102', 'aut_weyl_index': 27, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '9.b1.a1', '9.b1.b1', '9.b1.c1', '9.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6775, -1, 7670, -1, 6006, -1, 7271, -1], 'generators': [1, 108, 12, 2, 4], 'label': '324.20.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 65470366
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '9.d1.b1'], 'contains': ['36.d1.b1', '54.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1049, -1, 1601, -1, 1549, -1, 2206, -1], 'generators': [2, 256, 108], 'label': '324.20.18.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '18.d1.b1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470367
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '9.d1.c1'], 'contains': ['36.d1.c1', '54.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1049, -1, 2402, -1, 1549, -1, 2644, -1], 'generators': [2, 184, 108], 'label': '324.20.18.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.c1', 'old_label': '18.d1.c1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470368
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 972, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['36.e1.a1', '54.c1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5701, -1, 4395, -1, 5770, -1, 7893, -1], 'generators': [2, 4, 120], 'label': '324.20.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470369
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1458, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.b1.b1', '9.b1.c1'], 'contains': ['54.a1.a1', '81.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9347, -1, 8752, -1, 8850, -1, 8451, -1], 'generators': [1, 12, 2], 'label': '324.20.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470370
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.c1.a1', '9.d1.a1', '9.d1.b1', '9.d1.c1'], 'contains': ['54.b1.a1', '81.a1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6690, -1, 6024, -1, 6803, -1, 4617, -1], 'generators': [1, 2, 108], 'label': '324.20.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.b1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470371
    {'ambient': '324.20', 'aut_centralizer_order': 18, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.c1.a1'], 'contains': ['54.d1.a1', '81.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8573, -1, 8344, -1, 9665, -1, 9357, -1], 'generators': [1, 2, 4], 'label': '324.20.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '27.c1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470372
    {'ambient': '324.20', 'aut_centralizer_order': 18, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.b1', '9.c1.a1'], 'contains': ['54.d1.b1', '81.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8573, -1, 9162, -1, 9665, -1, 8899, -1], 'generators': [1, 2, 112], 'label': '324.20.27.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '27.c1.b1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470373
    {'ambient': '324.20', 'aut_centralizer_order': 18, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.c1', '9.c1.a1'], 'contains': ['54.d1.c1', '81.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8573, -1, 9581, -1, 9665, -1, 9816, -1], 'generators': [1, 2, 220], 'label': '324.20.27.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.c1', 'old_label': '27.c1.c1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470374
    {'ambient': '324.20', 'aut_centralizer_order': 1458, 'aut_label': '36.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1458, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '12.b1.c1', '18.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1350, 4782, 1556, 4016, 2283, 3708, 3078, 4385], 'generators': [12, 108], 'label': '324.20.36.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.b1', '12.b1.c1', '12.b1.a1', '18.a1.a1'], 'normal_contains': ['108.a1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '108.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470375
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': ['9.d1.a1', '9.d1.b1', '9.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.b1.a1'], 'contains': ['108.a1.a1', '108.d1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5701, 1522, 4031, 5680, 5163, 6970, 4253, 5881], 'generators': [4, 12], 'label': '324.20.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '18.b1.a1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470376
    {'ambient': '324.20', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.111', 'aut_weyl_index': 27, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.a1.a1', '9.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3836, -1, 4863, -1, 3859, -1, 5383, -1], 'generators': [1, 108, 12, 2, 36], 'label': '324.20.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470377
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': ['9.d1.a1', '9.d1.b1', '9.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.b1.b1'], 'contains': ['108.a1.a1', '108.d1.b1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5701, 1522, 4777, 4848, 5163, 6970, 3845, 8174], 'generators': [112, 12], 'label': '324.20.36.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.b1', 'normal_contained_in': ['12.a1.a1', '18.b1.b1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.b1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470378
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': ['9.d1.a1', '9.d1.b1', '9.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.b1.c1'], 'contains': ['108.a1.a1', '108.d1.c1'], 'core': '36.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5701, 1522, 5669, 6999, 5163, 6970, 5070, 7377], 'generators': [220, 12], 'label': '324.20.36.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.c1', 'normal_contained_in': ['12.a1.a1', '18.b1.c1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.c1', 'projective_image': '108.10', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470379
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 486, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.c1.a1'], 'contains': ['108.b1.a1', '108.d1.a1', '108.d1.b1', '108.d1.c1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2055, -1, 4403, -1, 3025, -1, 4661, -1], 'generators': [4, 108], 'label': '324.20.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470380
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.d1.a1'], 'contains': ['108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [688, -1, 878, -1, 1549, -1, 2694, -1], 'generators': [252], 'label': '324.20.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470381
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.d1.b1'], 'contains': ['108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [688, -1, 450, -1, 1549, -1, 1977, -1], 'generators': [256], 'label': '324.20.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '36.d1.b1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470382
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.c1', '18.d1.c1'], 'contains': ['108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [688, -1, 1205, -1, 1549, -1, 2336, -1], 'generators': [184], 'label': '324.20.36.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.c1', 'old_label': '36.d1.c1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470383
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 972, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.e1.a1'], 'contains': ['108.c1.a1', '108.d1.a1', '108.d1.b1', '108.d1.c1'], 'core': '324.a1.a1', 'coset_action_label': '36T488', 'count': 6, 'diagramx': [3087, -1, 3658, -1, 4420, -1, 5478, -1], 'generators': [4, 120], 'label': '324.20.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470384
    {'ambient': '324.20', 'aut_centralizer_order': 2916, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7524, 4782, 6242, 6289, 6513, 8602, 5861, 6629], 'generators': [2, 12], 'label': '324.20.54.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1'], 'normal_contains': ['108.a1.a1', '162.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '54.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '54.7', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470385
    {'ambient': '324.20', 'aut_centralizer_order': 2916, 'aut_label': '54.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.d1.c1', '27.b1.a1'], 'contains': ['108.b1.a1', '162.a1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4213, 6738, 2521, 3467, 3723, 5339, 3461, 5133], 'generators': [2, 108], 'label': '324.20.54.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.b1.a1', '162.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '162.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470386
    {'ambient': '324.20', 'aut_centralizer_order': 1458, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1'], 'contains': ['108.c1.a1', '162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4841, -1, 2848, -1, 5861, -1, 6220, -1], 'generators': [2, 120], 'label': '324.20.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470387
    {'ambient': '324.20', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.111', 'aut_weyl_index': 27, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '9.a1.a1', '9.d1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3836, -1, 4104, -1, 3859, -1, 3720, -1], 'generators': [1, 108, 12, 2, 64], 'label': '324.20.3.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '3.b1.b1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470388
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.c1.a1', '18.e1.a1', '27.c1.a1'], 'contains': ['108.d1.a1', '162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6578, -1, 5418, -1, 7165, -1, 6937, -1], 'generators': [2, 4], 'label': '324.20.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470389
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '18.c1.a1', '18.e1.a1', '27.c1.b1'], 'contains': ['108.d1.b1', '162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6578, -1, 6792, -1, 7165, -1, 6579, -1], 'generators': [2, 112], 'label': '324.20.54.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '54.d1.b1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470390
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '18.c1.a1', '18.e1.a1', '27.c1.c1'], 'contains': ['108.d1.c1', '162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6578, -1, 7511, -1, 7165, -1, 7296, -1], 'generators': [2, 220], 'label': '324.20.54.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '54.d1.c1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470391
    {'ambient': '324.20', 'aut_centralizer_order': 108, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1', '27.c1.b1', '27.c1.c1'], 'contains': ['162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8719, -1, 8576, -1, 8334, -1, 8675, -1], 'generators': [1], 'label': '324.20.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '162.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470392
    {'ambient': '324.20', 'aut_centralizer_order': 2916, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1', '54.a1.a1'], 'contains': ['324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5262, 3288, 4531, 5223, 4529, 6907, 4148, 6600], 'generators': [12], 'label': '324.20.108.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1', '54.a1.a1'], 'normal_contains': ['324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '108.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.10', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470393
    {'ambient': '324.20', 'aut_centralizer_order': 2916, 'aut_label': '108.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '54.b1.a1'], 'contains': ['324.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2055, 7309, 1556, 4025, 3025, 5339, 3078, 5133], 'generators': [108], 'label': '324.20.108.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.a1.a1', '54.b1.a1'], 'normal_contains': ['324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '324.20', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.10', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470395
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '36.e1.a1', '54.d1.a1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3861, -1, 4090, -1, 5181, -1, 5224, -1], 'generators': [4], 'label': '324.20.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470396
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.b1', '36.c1.a1', '36.e1.a1', '54.d1.b1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3861, -1, 4859, -1, 5181, -1, 4865, -1], 'generators': [112], 'label': '324.20.108.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.d1.b1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470397
    {'ambient': '324.20', 'aut_centralizer_order': 324, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2916, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.c1', '36.c1.a1', '36.e1.a1', '54.d1.c1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3861, -1, 5646, -1, 5181, -1, 5582, -1], 'generators': [220], 'label': '324.20.108.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.d1.c1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65470398
    {'ambient': '324.20', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.111', 'aut_weyl_index': 27, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '9.a1.a1', '9.d1.c1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3836, -1, 5791, -1, 3859, -1, 4552, -1], 'generators': [1, 108, 12, 2, 88], 'label': '324.20.3.b1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.c1', 'old_label': '3.b1.c1', 'projective_image': '54.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 65470399
    {'ambient': '324.20', 'aut_centralizer_order': 5832, 'aut_label': '162.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5832, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1', '81.a1.a1'], 'contains': ['324.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6458, 5163, 6251, 4635, 6187, 8432, 6399, 5881], 'generators': [2], 'label': '324.20.162.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': ['54.a1.a1', '54.b1.a1'], 'normal_contains': ['324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '162.17', 'quotient_action_image': '1.1', 'quotient_action_kernel': '162.17', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470400
    {'ambient': '324.20', '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': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.d1.b1', '108.d1.c1', '162.a1.a1'], 'contains': [], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3861, 5163, 4531, 4635, 4529, 6907, 4865, 5881], 'generators': [], 'label': '324.20.324.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.a1.a1', '108.b1.a1', '162.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '324.20', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65470401
    {'ambient': '324.20', 'aut_centralizer_order': 6, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '972.455', 'aut_weyl_index': 6, 'centralizer': '18.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '12.b1.c1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1161, 5136, 1406, 5457, 996, 1250, 1145, 2045], 'generators': [4, 252], 'label': '324.20.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.b1', '12.b1.c1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '108.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 65470402
    {'ambient': '324.20', 'aut_centralizer_order': 162, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 162, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '18.c1.a1', '18.e1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5168, 2038, 5582, 7243, 4538, 7563, 5632, 6649], 'generators': [2, 4, 12, 108], 'label': '324.20.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65470403
    {'ambient': '324.20', 'aut_centralizer_order': 54, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 162, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '18.a1.a1', '18.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2632, 8478, 2607, 2391, 2246, 4174, 3456, 4968], 'generators': [2, 12, 252, 108], 'label': '324.20.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '54.7', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}