Abstract group data - 1944.2443

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '18.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 2, 6, 12], 'aut_gens': [[1, 18, 54, 324], [425, 414, 1026, 1728], [1, 990, 270, 1620], [259, 900, 1242, 540], [1475, 1494, 270, 486]], 'aut_group': None, 'aut_hash': 81437165497806082, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 36, 'aut_perms': [289674156211165605333803757196975982007589, 10337068438666588966196507818668627336410, 18568066228459845492240083472107943592828, 108256356712426332800990540533285973912519], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 18, 1, 1], [3, 1, 2, 2], [3, 1, 4, 1], [3, 6, 1, 1], [3, 6, 2, 1], [3, 24, 3, 1], [3, 24, 6, 1], [4, 18, 1, 1], [6, 3, 2, 2], [6, 3, 4, 1], [6, 6, 1, 1], [6, 6, 2, 2], [6, 6, 4, 1], [6, 18, 2, 2], [6, 18, 4, 1], [9, 1, 18, 1], [9, 6, 6, 1], [9, 24, 18, 1], [12, 18, 2, 2], [12, 18, 4, 1], [18, 3, 18, 1], [18, 6, 18, 1], [18, 18, 18, 1], [36, 18, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2:C_3.C_3^2.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '18.3', 'autcent_hash': 3, 'autcent_nilpotent': False, 'autcent_order': 18, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3\\times S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 18, 1], [3, 1, 8], [3, 6, 3], [3, 24, 9], [4, 18, 1], [6, 3, 8], [6, 6, 9], [6, 18, 8], [9, 1, 18], [9, 6, 6], [9, 24, 18], [12, 18, 8], [18, 3, 18], [18, 6, 18], [18, 18, 18], [36, 18, 18]], 'center_label': '27.2', 'center_order': 27, 'central_product': True, 'central_quotient': '72.43', 'commutator_count': 2, 'commutator_label': '108.22', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2443, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['216.95', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 18, 1, 1], [3, 1, 2, 4], [3, 6, 1, 1], [3, 6, 2, 1], [3, 24, 1, 3], [3, 24, 2, 3], [4, 18, 1, 1], [6, 3, 2, 4], [6, 6, 1, 1], [6, 6, 2, 4], [6, 18, 2, 4], [9, 1, 6, 3], [9, 6, 6, 1], [9, 24, 6, 3], [12, 18, 2, 4], [18, 3, 6, 3], [18, 6, 6, 3], [18, 18, 6, 3], [36, 18, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 442260, 'exponent': 36, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '216.164', 'hash': 2443, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 6], 'inner_gens': [[1, 36, 54, 1782], [37, 18, 1026, 1350], [1, 990, 54, 324], [811, 1260, 54, 324]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_3:S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 18], [2, 36], [3, 90], [6, 27]], 'label': '1944.2443', 'linC_count': 432, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 12, 'linQ_dim': 12, 'linQ_dim_count': 12, 'linR_count': 108, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C9*C3^2:S4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 171, 'number_divisions': 52, 'number_normal_subgroups': 41, 'number_subgroup_autclasses': 171, 'number_subgroup_classes': 335, 'number_subgroups': 2010, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 21], [3, 242], [4, 18], [6, 222], [9, 486], [12, 144], [18, 486], [36, 324]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 6, 3], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 36, 270, 486], [17, 792, 54, 1782], [109, 18, 54, 324]], 'outer_group': '108.38', 'outer_hash': 38, 'outer_nilpotent': False, 'outer_order': 108, 'outer_permdeg': 9, 'outer_perms': [123121, 96004, 122424], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 6], [3, 2], [4, 4], [6, 17], [12, 8], [18, 10], [36, 3]], 'representations': {'PC': {'code': 20966496054568115427452701079691751536612213, 'gens': [1, 4, 5, 7], 'pres': [8, 2, 3, 3, 3, 2, 3, 2, 3, 16, 57, 1155, 2308, 116, 99798, 4230, 166, 82951, 2719]}, 'Perm': {'d': 22, 'gens': [512964039767558400, 58773835079511604023, 98356, 112420409816753740800, 165586057054209792000, 58773835079511552000, 482630400, 1037836800]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [18], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_9\\times C_3^2:S_4', 'transitive_degree': 162, '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: 136795068
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2443, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136795151
    {'aut_label': '2A', 'centralizer': '3.b1.a1', 'counter': 2, 'group_counter': 2443, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 972, 'size': 3}
  • id: 136795162
    {'aut_label': '2B', 'centralizer': '18.e1.a1', 'counter': 3, 'group_counter': 2443, 'group_order': 1944, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 9, 'size': 18}
  • id: 136795173
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 2443, 'group_order': 1944, 'label': '3A1', 'order': 3, 'powers': [5, 1], 'representative': 222, 'size': 1}
  • id: 136795184
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 2443, 'group_order': 1944, 'label': '3A-1', 'order': 3, 'powers': [4, 1], 'representative': 120, 'size': 1}
  • id: 136795195
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 2443, 'group_order': 1944, 'label': '3B1', 'order': 3, 'powers': [7, 1], 'representative': 114, 'size': 1}
  • id: 136795206
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 2443, 'group_order': 1944, 'label': '3B-1', 'order': 3, 'powers': [6, 1], 'representative': 228, 'size': 1}
  • id: 136795217
    {'aut_label': '3C1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 2443, 'group_order': 1944, 'label': '3C1', 'order': 3, 'powers': [9, 1], 'representative': 216, 'size': 1}
  • id: 136795228
    {'aut_label': '3C1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 2443, 'group_order': 1944, 'label': '3C-1', 'order': 3, 'powers': [8, 1], 'representative': 108, 'size': 1}
  • id: 136795069
    {'aut_label': '3D1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 2443, 'group_order': 1944, 'label': '3D1', 'order': 3, 'powers': [11, 1], 'representative': 6, 'size': 1}
  • id: 136795080
    {'aut_label': '3D1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 2443, 'group_order': 1944, 'label': '3D-1', 'order': 3, 'powers': [10, 1], 'representative': 12, 'size': 1}
  • id: 136795091
    {'aut_label': '3E', 'centralizer': '6.b1.a1', 'counter': 12, 'group_counter': 2443, 'group_order': 1944, 'label': '3E', 'order': 3, 'powers': [12, 1], 'representative': 864, 'size': 6}
  • id: 136795102
    {'aut_label': '3F1', 'centralizer': '6.b1.a1', 'counter': 13, 'group_counter': 2443, 'group_order': 1944, 'label': '3F1', 'order': 3, 'powers': [14, 1], 'representative': 660, 'size': 6}
  • id: 136795113
    {'aut_label': '3F1', 'centralizer': '6.b1.a1', 'counter': 14, 'group_counter': 2443, 'group_order': 1944, 'label': '3F-1', 'order': 3, 'powers': [13, 1], 'representative': 1302, 'size': 6}
  • id: 136795124
    {'aut_label': '3G', 'centralizer': '24.d1.a1', 'counter': 15, 'group_counter': 2443, 'group_order': 1944, 'label': '3G', 'order': 3, 'powers': [15, 1], 'representative': 18, 'size': 24}
  • id: 136795135
    {'aut_label': '3G', 'centralizer': '24.d1.b1', 'counter': 16, 'group_counter': 2443, 'group_order': 1944, 'label': '3H', 'order': 3, 'powers': [16, 1], 'representative': 666, 'size': 24}
  • id: 136795146
    {'aut_label': '3G', 'centralizer': '24.d1.c1', 'counter': 17, 'group_counter': 2443, 'group_order': 1944, 'label': '3I', 'order': 3, 'powers': [17, 1], 'representative': 342, 'size': 24}
  • id: 136795149
    {'aut_label': '3J1', 'centralizer': '24.d1.a1', 'counter': 18, 'group_counter': 2443, 'group_order': 1944, 'label': '3J1', 'order': 3, 'powers': [19, 1], 'representative': 24, 'size': 24}
  • id: 136795150
    {'aut_label': '3J1', 'centralizer': '24.d1.a1', 'counter': 19, 'group_counter': 2443, 'group_order': 1944, 'label': '3J-1', 'order': 3, 'powers': [18, 1], 'representative': 30, 'size': 24}
  • id: 136795152
    {'aut_label': '3J1', 'centralizer': '24.d1.b1', 'counter': 20, 'group_counter': 2443, 'group_order': 1944, 'label': '3K1', 'order': 3, 'powers': [21, 1], 'representative': 672, 'size': 24}
  • id: 136795153
    {'aut_label': '3J1', 'centralizer': '24.d1.b1', 'counter': 21, 'group_counter': 2443, 'group_order': 1944, 'label': '3K-1', 'order': 3, 'powers': [20, 1], 'representative': 678, 'size': 24}
  • id: 136795154
    {'aut_label': '3J1', 'centralizer': '24.d1.c1', 'counter': 22, 'group_counter': 2443, 'group_order': 1944, 'label': '3L1', 'order': 3, 'powers': [23, 1], 'representative': 348, 'size': 24}
  • id: 136795155
    {'aut_label': '3J1', 'centralizer': '24.d1.c1', 'counter': 23, 'group_counter': 2443, 'group_order': 1944, 'label': '3L-1', 'order': 3, 'powers': [22, 1], 'representative': 354, 'size': 24}
  • id: 136795156
    {'aut_label': '4A', 'centralizer': '18.i1.a1', 'counter': 24, 'group_counter': 2443, 'group_order': 1944, 'label': '4A', 'order': 4, 'powers': [2, 24], 'representative': 495, 'size': 18}
  • id: 136795157
    {'aut_label': '6A1', 'centralizer': '3.b1.a1', 'counter': 25, 'group_counter': 2443, 'group_order': 1944, 'label': '6A1', 'order': 6, 'powers': [5, 2], 'representative': 60, 'size': 3}
  • id: 136795158
    {'aut_label': '6A1', 'centralizer': '3.b1.a1', 'counter': 26, 'group_counter': 2443, 'group_order': 1944, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 282, 'size': 3}
  • id: 136795159
    {'aut_label': '6A1', 'centralizer': '3.b1.a1', 'counter': 27, 'group_counter': 2443, 'group_order': 1944, 'label': '6B1', 'order': 6, 'powers': [7, 2], 'representative': 276, 'size': 3}
  • id: 136795160
    {'aut_label': '6A1', 'centralizer': '3.b1.a1', 'counter': 28, 'group_counter': 2443, 'group_order': 1944, 'label': '6B-1', 'order': 6, 'powers': [6, 2], 'representative': 66, 'size': 3}
  • id: 136795161
    {'aut_label': '6C1', 'centralizer': '3.b1.a1', 'counter': 29, 'group_counter': 2443, 'group_order': 1944, 'label': '6C1', 'order': 6, 'powers': [9, 2], 'representative': 54, 'size': 3}
  • id: 136795163
    {'aut_label': '6C1', 'centralizer': '3.b1.a1', 'counter': 30, 'group_counter': 2443, 'group_order': 1944, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 270, 'size': 3}
  • id: 136795164
    {'aut_label': '6D1', 'centralizer': '3.b1.a1', 'counter': 31, 'group_counter': 2443, 'group_order': 1944, 'label': '6D1', 'order': 6, 'powers': [11, 2], 'representative': 978, 'size': 3}
  • id: 136795165
    {'aut_label': '6D1', 'centralizer': '3.b1.a1', 'counter': 32, 'group_counter': 2443, 'group_order': 1944, 'label': '6D-1', 'order': 6, 'powers': [10, 2], 'representative': 984, 'size': 3}
  • id: 136795166
    {'aut_label': '6E', 'centralizer': '6.b1.a1', 'counter': 33, 'group_counter': 2443, 'group_order': 1944, 'label': '6E', 'order': 6, 'powers': [12, 2], 'representative': 432, 'size': 6}
  • id: 136795167
    {'aut_label': '6F1', 'centralizer': '6.b1.a1', 'counter': 34, 'group_counter': 2443, 'group_order': 1944, 'label': '6F1', 'order': 6, 'powers': [12, 2], 'representative': 324, 'size': 6}
  • id: 136795168
    {'aut_label': '6F1', 'centralizer': '6.b1.a1', 'counter': 35, 'group_counter': 2443, 'group_order': 1944, 'label': '6F-1', 'order': 6, 'powers': [12, 2], 'representative': 1620, 'size': 6}
  • id: 136795169
    {'aut_label': '6G1', 'centralizer': '6.b1.a1', 'counter': 36, 'group_counter': 2443, 'group_order': 1944, 'label': '6G1', 'order': 6, 'powers': [13, 2], 'representative': 330, 'size': 6}
  • id: 136795170
    {'aut_label': '6G1', 'centralizer': '6.b1.a1', 'counter': 37, 'group_counter': 2443, 'group_order': 1944, 'label': '6G-1', 'order': 6, 'powers': [14, 2], 'representative': 1632, 'size': 6}
  • id: 136795171
    {'aut_label': '6G1', 'centralizer': '6.b1.a1', 'counter': 38, 'group_counter': 2443, 'group_order': 1944, 'label': '6H1', 'order': 6, 'powers': [14, 2], 'representative': 336, 'size': 6}
  • id: 136795172
    {'aut_label': '6G1', 'centralizer': '6.b1.a1', 'counter': 39, 'group_counter': 2443, 'group_order': 1944, 'label': '6H-1', 'order': 6, 'powers': [13, 2], 'representative': 1626, 'size': 6}
  • id: 136795174
    {'aut_label': '6I1', 'centralizer': '6.b1.a1', 'counter': 40, 'group_counter': 2443, 'group_order': 1944, 'label': '6I1', 'order': 6, 'powers': [13, 2], 'representative': 438, 'size': 6}
  • id: 136795175
    {'aut_label': '6I1', 'centralizer': '6.b1.a1', 'counter': 41, 'group_counter': 2443, 'group_order': 1944, 'label': '6I-1', 'order': 6, 'powers': [14, 2], 'representative': 444, 'size': 6}
  • id: 136795176
    {'aut_label': '6J1', 'centralizer': '18.e1.a1', 'counter': 42, 'group_counter': 2443, 'group_order': 1944, 'label': '6J1', 'order': 6, 'powers': [4, 3], 'representative': 111, 'size': 18}
  • id: 136795177
    {'aut_label': '6J1', 'centralizer': '18.e1.a1', 'counter': 43, 'group_counter': 2443, 'group_order': 1944, 'label': '6J-1', 'order': 6, 'powers': [5, 3], 'representative': 69, 'size': 18}
  • id: 136795178
    {'aut_label': '6J1', 'centralizer': '18.e1.a1', 'counter': 44, 'group_counter': 2443, 'group_order': 1944, 'label': '6K1', 'order': 6, 'powers': [6, 3], 'representative': 57, 'size': 18}
  • id: 136795179
    {'aut_label': '6J1', 'centralizer': '18.e1.a1', 'counter': 45, 'group_counter': 2443, 'group_order': 1944, 'label': '6K-1', 'order': 6, 'powers': [7, 3], 'representative': 123, 'size': 18}
  • id: 136795180
    {'aut_label': '6L1', 'centralizer': '18.e1.a1', 'counter': 46, 'group_counter': 2443, 'group_order': 1944, 'label': '6L1', 'order': 6, 'powers': [8, 3], 'representative': 117, 'size': 18}
  • id: 136795181
    {'aut_label': '6L1', 'centralizer': '18.e1.a1', 'counter': 47, 'group_counter': 2443, 'group_order': 1944, 'label': '6L-1', 'order': 6, 'powers': [9, 3], 'representative': 63, 'size': 18}
  • id: 136795182
    {'aut_label': '6M1', 'centralizer': '18.e1.a1', 'counter': 48, 'group_counter': 2443, 'group_order': 1944, 'label': '6M1', 'order': 6, 'powers': [10, 3], 'representative': 3, 'size': 18}
  • id: 136795183
    {'aut_label': '6M1', 'centralizer': '18.e1.a1', 'counter': 49, 'group_counter': 2443, 'group_order': 1944, 'label': '6M-1', 'order': 6, 'powers': [11, 3], 'representative': 15, 'size': 18}
  • id: 136795185
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 50, 'group_counter': 2443, 'group_order': 1944, 'label': '9A1', 'order': 9, 'powers': [52, 10], 'representative': 2, 'size': 1}
  • id: 136795186
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 51, 'group_counter': 2443, 'group_order': 1944, 'label': '9A-1', 'order': 9, 'powers': [53, 11], 'representative': 16, 'size': 1}
  • id: 136795187
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 52, 'group_counter': 2443, 'group_order': 1944, 'label': '9A2', 'order': 9, 'powers': [54, 11], 'representative': 4, 'size': 1}
  • id: 136795188
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 2443, 'group_order': 1944, 'label': '9A-2', 'order': 9, 'powers': [55, 10], 'representative': 14, 'size': 1}
  • id: 136795189
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 54, 'group_counter': 2443, 'group_order': 1944, 'label': '9A4', 'order': 9, 'powers': [51, 10], 'representative': 8, 'size': 1}
  • id: 136795190
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 55, 'group_counter': 2443, 'group_order': 1944, 'label': '9A-4', 'order': 9, 'powers': [50, 11], 'representative': 10, 'size': 1}
  • id: 136795191
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 56, 'group_counter': 2443, 'group_order': 1944, 'label': '9B1', 'order': 9, 'powers': [58, 10], 'representative': 218, 'size': 1}
  • id: 136795192
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 57, 'group_counter': 2443, 'group_order': 1944, 'label': '9B-1', 'order': 9, 'powers': [59, 11], 'representative': 124, 'size': 1}
  • id: 136795193
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 58, 'group_counter': 2443, 'group_order': 1944, 'label': '9B2', 'order': 9, 'powers': [60, 11], 'representative': 112, 'size': 1}
  • id: 136795194
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 59, 'group_counter': 2443, 'group_order': 1944, 'label': '9B-2', 'order': 9, 'powers': [61, 10], 'representative': 230, 'size': 1}
  • id: 136795196
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 60, 'group_counter': 2443, 'group_order': 1944, 'label': '9B4', 'order': 9, 'powers': [57, 10], 'representative': 224, 'size': 1}
  • id: 136795197
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 61, 'group_counter': 2443, 'group_order': 1944, 'label': '9B-4', 'order': 9, 'powers': [56, 11], 'representative': 118, 'size': 1}
  • id: 136795198
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 62, 'group_counter': 2443, 'group_order': 1944, 'label': '9C1', 'order': 9, 'powers': [64, 10], 'representative': 110, 'size': 1}
  • id: 136795199
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 63, 'group_counter': 2443, 'group_order': 1944, 'label': '9C-1', 'order': 9, 'powers': [65, 11], 'representative': 232, 'size': 1}
  • id: 136795200
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 64, 'group_counter': 2443, 'group_order': 1944, 'label': '9C2', 'order': 9, 'powers': [66, 11], 'representative': 220, 'size': 1}
  • id: 136795201
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 65, 'group_counter': 2443, 'group_order': 1944, 'label': '9C-2', 'order': 9, 'powers': [67, 10], 'representative': 122, 'size': 1}
  • id: 136795202
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 66, 'group_counter': 2443, 'group_order': 1944, 'label': '9C4', 'order': 9, 'powers': [63, 10], 'representative': 116, 'size': 1}
  • id: 136795203
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 67, 'group_counter': 2443, 'group_order': 1944, 'label': '9C-4', 'order': 9, 'powers': [62, 11], 'representative': 226, 'size': 1}
  • id: 136795204
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 68, 'group_counter': 2443, 'group_order': 1944, 'label': '9D1', 'order': 9, 'powers': [70, 11], 'representative': 652, 'size': 6}
  • id: 136795205
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 69, 'group_counter': 2443, 'group_order': 1944, 'label': '9D-1', 'order': 9, 'powers': [71, 10], 'representative': 1310, 'size': 6}
  • id: 136795207
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 70, 'group_counter': 2443, 'group_order': 1944, 'label': '9D2', 'order': 9, 'powers': [72, 10], 'representative': 1304, 'size': 6}
  • id: 136795208
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 71, 'group_counter': 2443, 'group_order': 1944, 'label': '9D-2', 'order': 9, 'powers': [73, 11], 'representative': 658, 'size': 6}
  • id: 136795209
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 72, 'group_counter': 2443, 'group_order': 1944, 'label': '9D4', 'order': 9, 'powers': [69, 11], 'representative': 664, 'size': 6}
  • id: 136795210
    {'aut_label': '9D1', 'centralizer': '6.b1.a1', 'counter': 73, 'group_counter': 2443, 'group_order': 1944, 'label': '9D-4', 'order': 9, 'powers': [68, 10], 'representative': 1298, 'size': 6}
  • id: 136795211
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 74, 'group_counter': 2443, 'group_order': 1944, 'label': '9E1', 'order': 9, 'powers': [76, 10], 'representative': 20, 'size': 24}
  • id: 136795212
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 75, 'group_counter': 2443, 'group_order': 1944, 'label': '9E-1', 'order': 9, 'powers': [77, 11], 'representative': 34, 'size': 24}
  • id: 136795213
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 76, 'group_counter': 2443, 'group_order': 1944, 'label': '9E2', 'order': 9, 'powers': [78, 11], 'representative': 22, 'size': 24}
  • id: 136795214
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 77, 'group_counter': 2443, 'group_order': 1944, 'label': '9E-2', 'order': 9, 'powers': [79, 10], 'representative': 32, 'size': 24}
  • id: 136795215
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 78, 'group_counter': 2443, 'group_order': 1944, 'label': '9E4', 'order': 9, 'powers': [75, 10], 'representative': 26, 'size': 24}
  • id: 136795216
    {'aut_label': '9E1', 'centralizer': '24.d1.a1', 'counter': 79, 'group_counter': 2443, 'group_order': 1944, 'label': '9E-4', 'order': 9, 'powers': [74, 11], 'representative': 28, 'size': 24}
  • id: 136795218
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 80, 'group_counter': 2443, 'group_order': 1944, 'label': '9F1', 'order': 9, 'powers': [82, 10], 'representative': 668, 'size': 24}
  • id: 136795219
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 81, 'group_counter': 2443, 'group_order': 1944, 'label': '9F-1', 'order': 9, 'powers': [83, 11], 'representative': 682, 'size': 24}
  • id: 136795220
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 82, 'group_counter': 2443, 'group_order': 1944, 'label': '9F2', 'order': 9, 'powers': [84, 11], 'representative': 670, 'size': 24}
  • id: 136795221
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 83, 'group_counter': 2443, 'group_order': 1944, 'label': '9F-2', 'order': 9, 'powers': [85, 10], 'representative': 680, 'size': 24}
  • id: 136795222
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 84, 'group_counter': 2443, 'group_order': 1944, 'label': '9F4', 'order': 9, 'powers': [81, 10], 'representative': 674, 'size': 24}
  • id: 136795223
    {'aut_label': '9E1', 'centralizer': '24.d1.b1', 'counter': 85, 'group_counter': 2443, 'group_order': 1944, 'label': '9F-4', 'order': 9, 'powers': [80, 11], 'representative': 676, 'size': 24}
  • id: 136795224
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 86, 'group_counter': 2443, 'group_order': 1944, 'label': '9G1', 'order': 9, 'powers': [88, 10], 'representative': 344, 'size': 24}
  • id: 136795225
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 87, 'group_counter': 2443, 'group_order': 1944, 'label': '9G-1', 'order': 9, 'powers': [89, 11], 'representative': 358, 'size': 24}
  • id: 136795226
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 88, 'group_counter': 2443, 'group_order': 1944, 'label': '9G2', 'order': 9, 'powers': [90, 11], 'representative': 346, 'size': 24}
  • id: 136795227
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 89, 'group_counter': 2443, 'group_order': 1944, 'label': '9G-2', 'order': 9, 'powers': [91, 10], 'representative': 356, 'size': 24}
  • id: 136795229
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 90, 'group_counter': 2443, 'group_order': 1944, 'label': '9G4', 'order': 9, 'powers': [87, 10], 'representative': 350, 'size': 24}
  • id: 136795230
    {'aut_label': '9E1', 'centralizer': '24.d1.c1', 'counter': 91, 'group_counter': 2443, 'group_order': 1944, 'label': '9G-4', 'order': 9, 'powers': [86, 11], 'representative': 352, 'size': 24}
  • id: 136795231
    {'aut_label': '12A1', 'centralizer': '18.i1.a1', 'counter': 92, 'group_counter': 2443, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [25, 24], 'representative': 435, 'size': 18}
  • id: 136795232
    {'aut_label': '12A1', 'centralizer': '18.i1.a1', 'counter': 93, 'group_counter': 2443, 'group_order': 1944, 'label': '12A-1', 'order': 12, 'powers': [26, 24], 'representative': 393, 'size': 18}
  • id: 136795233
    {'aut_label': '12A1', 'centralizer': '18.i1.a1', 'counter': 94, 'group_counter': 2443, 'group_order': 1944, 'label': '12B1', 'order': 12, 'powers': [27, 24], 'representative': 381, 'size': 18}
  • id: 136795234
    {'aut_label': '12A1', 'centralizer': '18.i1.a1', 'counter': 95, 'group_counter': 2443, 'group_order': 1944, 'label': '12B-1', 'order': 12, 'powers': [28, 24], 'representative': 447, 'size': 18}
  • id: 136795235
    {'aut_label': '12C1', 'centralizer': '18.i1.a1', 'counter': 96, 'group_counter': 2443, 'group_order': 1944, 'label': '12C1', 'order': 12, 'powers': [29, 24], 'representative': 441, 'size': 18}
  • id: 136795236
    {'aut_label': '12C1', 'centralizer': '18.i1.a1', 'counter': 97, 'group_counter': 2443, 'group_order': 1944, 'label': '12C-1', 'order': 12, 'powers': [30, 24], 'representative': 387, 'size': 18}
  • id: 136795237
    {'aut_label': '12D1', 'centralizer': '18.i1.a1', 'counter': 98, 'group_counter': 2443, 'group_order': 1944, 'label': '12D1', 'order': 12, 'powers': [31, 24], 'representative': 489, 'size': 18}
  • id: 136795238
    {'aut_label': '12D1', 'centralizer': '18.i1.a1', 'counter': 99, 'group_counter': 2443, 'group_order': 1944, 'label': '12D-1', 'order': 12, 'powers': [32, 24], 'representative': 339, 'size': 18}
  • id: 136795070
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 100, 'group_counter': 2443, 'group_order': 1944, 'label': '18A1', 'order': 18, 'powers': [52, 31], 'representative': 164, 'size': 3}
  • id: 136795071
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 101, 'group_counter': 2443, 'group_order': 1944, 'label': '18A-1', 'order': 18, 'powers': [53, 32], 'representative': 178, 'size': 3}
  • id: 136795072
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 102, 'group_counter': 2443, 'group_order': 1944, 'label': '18A5', 'order': 18, 'powers': [50, 32], 'representative': 172, 'size': 3}
  • id: 136795073
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 103, 'group_counter': 2443, 'group_order': 1944, 'label': '18A-5', 'order': 18, 'powers': [51, 31], 'representative': 170, 'size': 3}
  • id: 136795074
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 104, 'group_counter': 2443, 'group_order': 1944, 'label': '18A7', 'order': 18, 'powers': [55, 31], 'representative': 176, 'size': 3}
  • id: 136795075
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 105, 'group_counter': 2443, 'group_order': 1944, 'label': '18A-7', 'order': 18, 'powers': [54, 32], 'representative': 166, 'size': 3}
  • id: 136795076
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 106, 'group_counter': 2443, 'group_order': 1944, 'label': '18B1', 'order': 18, 'powers': [58, 31], 'representative': 56, 'size': 3}
  • id: 136795077
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 107, 'group_counter': 2443, 'group_order': 1944, 'label': '18B-1', 'order': 18, 'powers': [59, 32], 'representative': 286, 'size': 3}
  • id: 136795078
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 108, 'group_counter': 2443, 'group_order': 1944, 'label': '18B5', 'order': 18, 'powers': [56, 32], 'representative': 280, 'size': 3}
  • id: 136795079
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 109, 'group_counter': 2443, 'group_order': 1944, 'label': '18B-5', 'order': 18, 'powers': [57, 31], 'representative': 62, 'size': 3}
  • id: 136795081
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 110, 'group_counter': 2443, 'group_order': 1944, 'label': '18B7', 'order': 18, 'powers': [61, 31], 'representative': 68, 'size': 3}
  • id: 136795082
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 111, 'group_counter': 2443, 'group_order': 1944, 'label': '18B-7', 'order': 18, 'powers': [60, 32], 'representative': 274, 'size': 3}
  • id: 136795083
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 112, 'group_counter': 2443, 'group_order': 1944, 'label': '18C1', 'order': 18, 'powers': [64, 31], 'representative': 272, 'size': 3}
  • id: 136795084
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 113, 'group_counter': 2443, 'group_order': 1944, 'label': '18C-1', 'order': 18, 'powers': [65, 32], 'representative': 70, 'size': 3}
  • id: 136795085
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 114, 'group_counter': 2443, 'group_order': 1944, 'label': '18C5', 'order': 18, 'powers': [62, 32], 'representative': 64, 'size': 3}
  • id: 136795086
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 115, 'group_counter': 2443, 'group_order': 1944, 'label': '18C-5', 'order': 18, 'powers': [63, 31], 'representative': 278, 'size': 3}
  • id: 136795087
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 116, 'group_counter': 2443, 'group_order': 1944, 'label': '18C7', 'order': 18, 'powers': [67, 31], 'representative': 284, 'size': 3}
  • id: 136795088
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 117, 'group_counter': 2443, 'group_order': 1944, 'label': '18C-7', 'order': 18, 'powers': [66, 32], 'representative': 58, 'size': 3}
  • id: 136795089
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 118, 'group_counter': 2443, 'group_order': 1944, 'label': '18D1', 'order': 18, 'powers': [68, 31], 'representative': 326, 'size': 6}
  • id: 136795090
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 119, 'group_counter': 2443, 'group_order': 1944, 'label': '18D-1', 'order': 18, 'powers': [69, 32], 'representative': 1636, 'size': 6}
  • id: 136795092
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 120, 'group_counter': 2443, 'group_order': 1944, 'label': '18D5', 'order': 18, 'powers': [73, 32], 'representative': 1630, 'size': 6}
  • id: 136795093
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 121, 'group_counter': 2443, 'group_order': 1944, 'label': '18D-5', 'order': 18, 'powers': [72, 31], 'representative': 332, 'size': 6}
  • id: 136795094
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 122, 'group_counter': 2443, 'group_order': 1944, 'label': '18D7', 'order': 18, 'powers': [71, 31], 'representative': 338, 'size': 6}
  • id: 136795095
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 123, 'group_counter': 2443, 'group_order': 1944, 'label': '18D-7', 'order': 18, 'powers': [70, 32], 'representative': 1624, 'size': 6}
  • id: 136795096
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 124, 'group_counter': 2443, 'group_order': 1944, 'label': '18E1', 'order': 18, 'powers': [70, 32], 'representative': 328, 'size': 6}
  • id: 136795097
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 125, 'group_counter': 2443, 'group_order': 1944, 'label': '18E-1', 'order': 18, 'powers': [71, 31], 'representative': 1634, 'size': 6}
  • id: 136795098
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 126, 'group_counter': 2443, 'group_order': 1944, 'label': '18E5', 'order': 18, 'powers': [68, 31], 'representative': 1622, 'size': 6}
  • id: 136795099
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 127, 'group_counter': 2443, 'group_order': 1944, 'label': '18E-5', 'order': 18, 'powers': [69, 32], 'representative': 340, 'size': 6}
  • id: 136795100
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 128, 'group_counter': 2443, 'group_order': 1944, 'label': '18E7', 'order': 18, 'powers': [73, 32], 'representative': 334, 'size': 6}
  • id: 136795101
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 129, 'group_counter': 2443, 'group_order': 1944, 'label': '18E-7', 'order': 18, 'powers': [72, 31], 'representative': 1628, 'size': 6}
  • id: 136795103
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 130, 'group_counter': 2443, 'group_order': 1944, 'label': '18F1', 'order': 18, 'powers': [68, 31], 'representative': 434, 'size': 6}
  • id: 136795104
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 131, 'group_counter': 2443, 'group_order': 1944, 'label': '18F-1', 'order': 18, 'powers': [69, 32], 'representative': 448, 'size': 6}
  • id: 136795105
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 132, 'group_counter': 2443, 'group_order': 1944, 'label': '18F5', 'order': 18, 'powers': [73, 32], 'representative': 442, 'size': 6}
  • id: 136795106
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 133, 'group_counter': 2443, 'group_order': 1944, 'label': '18F-5', 'order': 18, 'powers': [72, 31], 'representative': 440, 'size': 6}
  • id: 136795107
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 134, 'group_counter': 2443, 'group_order': 1944, 'label': '18F7', 'order': 18, 'powers': [71, 31], 'representative': 446, 'size': 6}
  • id: 136795108
    {'aut_label': '18D1', 'centralizer': '6.b1.a1', 'counter': 135, 'group_counter': 2443, 'group_order': 1944, 'label': '18F-7', 'order': 18, 'powers': [70, 32], 'representative': 436, 'size': 6}
  • id: 136795109
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 136, 'group_counter': 2443, 'group_order': 1944, 'label': '18G1', 'order': 18, 'powers': [50, 48], 'representative': 1, 'size': 18}
  • id: 136795110
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 137, 'group_counter': 2443, 'group_order': 1944, 'label': '18G-1', 'order': 18, 'powers': [51, 49], 'representative': 17, 'size': 18}
  • id: 136795111
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 138, 'group_counter': 2443, 'group_order': 1944, 'label': '18G5', 'order': 18, 'powers': [55, 49], 'representative': 5, 'size': 18}
  • id: 136795112
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 139, 'group_counter': 2443, 'group_order': 1944, 'label': '18G-5', 'order': 18, 'powers': [54, 48], 'representative': 13, 'size': 18}
  • id: 136795114
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 140, 'group_counter': 2443, 'group_order': 1944, 'label': '18G7', 'order': 18, 'powers': [53, 48], 'representative': 7, 'size': 18}
  • id: 136795115
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 141, 'group_counter': 2443, 'group_order': 1944, 'label': '18G-7', 'order': 18, 'powers': [52, 49], 'representative': 11, 'size': 18}
  • id: 136795116
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 142, 'group_counter': 2443, 'group_order': 1944, 'label': '18H1', 'order': 18, 'powers': [56, 48], 'representative': 109, 'size': 18}
  • id: 136795117
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 143, 'group_counter': 2443, 'group_order': 1944, 'label': '18H-1', 'order': 18, 'powers': [57, 49], 'representative': 71, 'size': 18}
  • id: 136795118
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 144, 'group_counter': 2443, 'group_order': 1944, 'label': '18H5', 'order': 18, 'powers': [61, 49], 'representative': 59, 'size': 18}
  • id: 136795119
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 145, 'group_counter': 2443, 'group_order': 1944, 'label': '18H-5', 'order': 18, 'powers': [60, 48], 'representative': 121, 'size': 18}
  • id: 136795120
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 146, 'group_counter': 2443, 'group_order': 1944, 'label': '18H7', 'order': 18, 'powers': [59, 48], 'representative': 115, 'size': 18}
  • id: 136795121
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 147, 'group_counter': 2443, 'group_order': 1944, 'label': '18H-7', 'order': 18, 'powers': [58, 49], 'representative': 65, 'size': 18}
  • id: 136795122
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 148, 'group_counter': 2443, 'group_order': 1944, 'label': '18I1', 'order': 18, 'powers': [62, 48], 'representative': 55, 'size': 18}
  • id: 136795123
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 149, 'group_counter': 2443, 'group_order': 1944, 'label': '18I-1', 'order': 18, 'powers': [63, 49], 'representative': 125, 'size': 18}
  • id: 136795125
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 150, 'group_counter': 2443, 'group_order': 1944, 'label': '18I5', 'order': 18, 'powers': [67, 49], 'representative': 113, 'size': 18}
  • id: 136795126
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 151, 'group_counter': 2443, 'group_order': 1944, 'label': '18I-5', 'order': 18, 'powers': [66, 48], 'representative': 67, 'size': 18}
  • id: 136795127
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 152, 'group_counter': 2443, 'group_order': 1944, 'label': '18I7', 'order': 18, 'powers': [65, 48], 'representative': 61, 'size': 18}
  • id: 136795128
    {'aut_label': '18G1', 'centralizer': '18.e1.a1', 'counter': 153, 'group_counter': 2443, 'group_order': 1944, 'label': '18I-7', 'order': 18, 'powers': [64, 49], 'representative': 119, 'size': 18}
  • id: 136795129
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 154, 'group_counter': 2443, 'group_order': 1944, 'label': '36A1', 'order': 36, 'powers': [100, 98], 'representative': 325, 'size': 18}
  • id: 136795130
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 155, 'group_counter': 2443, 'group_order': 1944, 'label': '36A-1', 'order': 36, 'powers': [101, 99], 'representative': 341, 'size': 18}
  • id: 136795131
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 156, 'group_counter': 2443, 'group_order': 1944, 'label': '36A5', 'order': 36, 'powers': [102, 99], 'representative': 329, 'size': 18}
  • id: 136795132
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 157, 'group_counter': 2443, 'group_order': 1944, 'label': '36A-5', 'order': 36, 'powers': [103, 98], 'representative': 337, 'size': 18}
  • id: 136795133
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 158, 'group_counter': 2443, 'group_order': 1944, 'label': '36A7', 'order': 36, 'powers': [104, 98], 'representative': 331, 'size': 18}
  • id: 136795134
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 159, 'group_counter': 2443, 'group_order': 1944, 'label': '36A-7', 'order': 36, 'powers': [105, 99], 'representative': 335, 'size': 18}
  • id: 136795136
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 160, 'group_counter': 2443, 'group_order': 1944, 'label': '36B1', 'order': 36, 'powers': [106, 98], 'representative': 433, 'size': 18}
  • id: 136795137
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 161, 'group_counter': 2443, 'group_order': 1944, 'label': '36B-1', 'order': 36, 'powers': [107, 99], 'representative': 395, 'size': 18}
  • id: 136795138
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 162, 'group_counter': 2443, 'group_order': 1944, 'label': '36B5', 'order': 36, 'powers': [108, 99], 'representative': 383, 'size': 18}
  • id: 136795139
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 163, 'group_counter': 2443, 'group_order': 1944, 'label': '36B-5', 'order': 36, 'powers': [109, 98], 'representative': 445, 'size': 18}
  • id: 136795140
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 164, 'group_counter': 2443, 'group_order': 1944, 'label': '36B7', 'order': 36, 'powers': [110, 98], 'representative': 439, 'size': 18}
  • id: 136795141
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 165, 'group_counter': 2443, 'group_order': 1944, 'label': '36B-7', 'order': 36, 'powers': [111, 99], 'representative': 389, 'size': 18}
  • id: 136795142
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 166, 'group_counter': 2443, 'group_order': 1944, 'label': '36C1', 'order': 36, 'powers': [112, 98], 'representative': 379, 'size': 18}
  • id: 136795143
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 167, 'group_counter': 2443, 'group_order': 1944, 'label': '36C-1', 'order': 36, 'powers': [113, 99], 'representative': 449, 'size': 18}
  • id: 136795144
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 168, 'group_counter': 2443, 'group_order': 1944, 'label': '36C5', 'order': 36, 'powers': [114, 99], 'representative': 437, 'size': 18}
  • id: 136795145
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 169, 'group_counter': 2443, 'group_order': 1944, 'label': '36C-5', 'order': 36, 'powers': [115, 98], 'representative': 391, 'size': 18}
  • id: 136795147
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 170, 'group_counter': 2443, 'group_order': 1944, 'label': '36C7', 'order': 36, 'powers': [116, 98], 'representative': 385, 'size': 18}
  • id: 136795148
    {'aut_label': '36A1', 'centralizer': '18.i1.a1', 'counter': 171, 'group_counter': 2443, 'group_order': 1944, 'label': '36C-7', 'order': 36, 'powers': [117, 99], 'representative': 443, 'size': 18}
• 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: 12035941
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12035952
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12035963
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12035974
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12035990
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035991
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035992
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035942
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035951
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12035953
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12035943
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, 4, -2, 4, -2, -2, 4, -2, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035944
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, 4, -2, -2, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035945
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 4, -2, -2, 4, -2, -2, 4, -2, -2, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035946
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2h', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035985
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1e', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, 6, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035989
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.1f', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, -6, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, -6, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, -3, -3, 6, -3, 6, -3, -3, -6, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035954
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3c', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, 6, -3, -3, -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, -1, -1, -1, -1, 2, -1, 2, -1, -3, -3, 6, -3, -3, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2], 'schur_index': 1}
  • id: 12035955
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3d', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, -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, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, 6, 6, -3, -3, 6, 6, -3, 6, -3, -3, -3, -3, -3, -3, -3, -3, 6, -3, 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, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1], 'schur_index': 1}
  • id: 12035956
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3e', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, 6, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -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, -1, -1, -1, -1, 2, -1, 2, -1, -3, -3, -3, 6, -3, -3, 6, -3, 6, 6, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1], 'schur_index': 1}
  • id: 12035957
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3f', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, -2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12035958
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3g', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, 1, -2, 1, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, 6, -3, -3, -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, 1, 1, 1, 1, -2, 1, -2, 1, -3, -3, 6, -3, -3, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2], 'schur_index': 1}
  • id: 12035959
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3h', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, 1, -2, 1, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, -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, 0, 0, 1, 1, 1, 1, -2, 1, -2, 1, 6, 6, -3, -3, 6, 6, -3, 6, -3, -3, -3, -3, -3, -3, -3, -3, 6, -3, 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, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, 1], 'schur_index': 1}
  • id: 12035960
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3i', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, 1, -2, 1, 6, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -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, 1, 1, 1, 1, -2, 1, -2, 1, -3, -3, -3, 6, -3, -3, 6, -3, 6, 6, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1], 'schur_index': 1}
  • id: 12035961
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3j', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12035962
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3k', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, 1, 1, 1, 1, -2, 1, -2, 1, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, 6, -3, -3, -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, -1, -1, -1, -1, 2, -1, 2, -1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, 1, -2, -2, 4, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, 4, -2, 4, 4, -2, -2, -2, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2], 'schur_index': 1}
  • id: 12035964
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3l', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, 1, 1, 1, 1, -2, 1, -2, 1, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, -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, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, -2, -2, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1], 'schur_index': 1}
  • id: 12035965
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3m', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, 1, 1, 1, 1, -2, 1, -2, 1, 6, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -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, -1, -1, -1, -1, 2, -1, 2, -1, 1, 1, 1, -2, 1, 1, -2, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, 4, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, 4, -2, 1, -2, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1], 'schur_index': 1}
  • id: 12035966
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3n', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, -1, -1, -1, -1, 2, -1, 2, -1, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, 6, -3, -3, -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, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, 1, -2, -2, 4, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, 4, -2, 4, 4, -2, -2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2], 'schur_index': 1}
  • id: 12035967
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3o', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, -1, -1, -1, -1, 2, -1, 2, -1, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, -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, 0, 0, 1, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, 1], 'schur_index': 1}
  • id: 12035968
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3p', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, -2, -2, 4, -2, -2, 4, -1, -1, -1, -1, 2, -1, 2, -1, 6, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -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, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, 1, -2, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 4, -2, -2, 4, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, 4, -2, -1, 2, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 1, 1, -2, 1, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1], 'schur_index': 1}
  • id: 12035980
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6a', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035947
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2i', 'multiplicity': 6, 'nt': [18, 16], 'qdim': 12, 'qvalues': [12, 12, 0, -6, -6, -6, 12, 12, -6, -6, -6, -6, -6, 12, 3, -6, 3, 3, 3, 3, -6, -6, 3, 0, -6, -6, -6, -6, 12, 12, -6, -6, 12, -6, -6, -6, 12, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035948
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2j', 'multiplicity': 6, 'nt': [18, 16], 'qdim': 12, 'qvalues': [12, 12, 0, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, -6, -6, -6, 3, -6, 3, 3, 12, -6, 3, 0, -6, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, 3, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035949
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2k', 'multiplicity': 6, 'nt': [18, 16], 'qdim': 12, 'qvalues': [12, 12, 0, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, -6, 3, -6, -6, 3, -6, 3, -6, 12, 3, 0, -6, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, 3, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035950
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.2l', 'multiplicity': 6, 'nt': [18, 16], 'qdim': 12, 'qvalues': [12, 12, 0, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, -6, 3, 12, 3, 3, 3, -6, -6, -6, -6, 0, -6, -6, -6, -6, 12, 12, -6, -6, -6, 3, 3, 3, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035981
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6b', 'multiplicity': 2, 'nt': [24, 564], 'qdim': 12, 'qvalues': [12, -4, 0, 12, 12, 12, 12, 12, 12, 12, 12, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035982
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6c', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, 12, -6, -6, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, -4, 2, 2, 2, 2, -4, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 12, -6, -6, -6, -6, 12, 12, -6, -6, 12, 12, 12, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, -4, -4, 2, -4, 2, -4, 2, 2, 2, 2, 2, -4, 2, 2, 2, -4, -4, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035983
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6d', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, 12, -6, -6, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, -4, 2, 2, 2, 2, -4, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, -6, -6, 12, 12, -6, -6, -6, -6, 12, -6, -6, -6, 12, -6, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, -4, -4, 2, -4, 2, 2, 2, 2, 2, 2, 2, 2, -4, 2, 2, 2, -4, 2, 2, 2, -4, 2, 2, -4, -4, 2, 2, -4, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035984
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6e', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, 12, -6, -6, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, -4, 2, 2, 2, 2, -4, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, 12, -6, -6, 12, -6, -6, 12, -6, -6, -6, -6, -6, 12, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, 2, 2, -4, 2, -4, -4, 2, 2, -4, -4, 2, 2, 2, 2, -4, 2, 2, -4, -4, -4, 2, 2, -4, 2, 2, 2, 2, 2, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035969
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3q', 'multiplicity': 6, 'nt': [27, 39], 'qdim': 18, 'qvalues': [18, 18, 6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 18, 18, -9, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035970
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3r', 'multiplicity': 6, 'nt': [27, 39], 'qdim': 18, 'qvalues': [18, 18, 6, -9, 18, 18, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035971
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3s', 'multiplicity': 6, 'nt': [36, 304], 'qdim': 18, 'qvalues': [18, -6, 6, -9, -9, -9, 18, 18, -9, -9, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 3, 3, 3, -6, -6, 3, 3, -6, 3, 3, 3, -6, 3, -6, 3, 3, 6, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035972
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3t', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, -6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, -6, 3, 3, 3, 3, 3, 3, 12, 12, -6, -6, -6, -6, -6, 12, -6, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035973
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3u', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, -6, -9, -9, -9, 18, 18, -9, -9, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 3, 3, 3, -6, -6, 3, 3, -6, 3, 3, 3, -6, 3, -6, 3, 3, -6, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035975
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3v', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, -6, -9, 18, 18, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 3, 3, 3, 3, 3, -6, -6, 12, -6, 12, 12, -6, -6, -6, -6, -6, 3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035976
    {'cdim': 3, 'counter': 41, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3w', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 3, 3, 3, 3, 12, 12, -6, -6, -6, -6, -6, 12, -6, -3, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035977
    {'cdim': 3, 'counter': 42, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3x', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 6, -9, 18, 18, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 3, 3, 3, 3, 3, -6, -6, 12, -6, 12, 12, -6, -6, -6, -6, -6, -3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035978
    {'cdim': 3, 'counter': 43, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3y', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, -6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 18, 18, -9, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12035979
    {'cdim': 3, 'counter': 44, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.3z', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, -6, -9, 18, 18, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -9, -9, -9, -9, -9, -9, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035986
    {'cdim': 6, 'counter': 50, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6f', 'multiplicity': 6, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, -12, 0, -18, -18, -18, 36, 36, -18, -18, -18, 9, 9, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, -12, -12, 6, 6, 6, -3, -3, -3, 6, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035987
    {'cdim': 6, 'counter': 51, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6g', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 0, -18, -18, -18, -18, -18, -18, 36, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 6, 6, 6, 6, 6, -12, -12, 6, 6, 6, 6, 6, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12035988
    {'cdim': 6, 'counter': 52, 'faithful': False, 'group': '1944.2443', 'group_order': 1944, 'image': None, 'label': '1944.2443.6h', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 0, -18, 36, 36, -18, -18, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -12, -12, -12, 6, -12, -12, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 27523963
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1944, 'label': '1944.2443.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 27524046
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  • id: 27524057
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  • id: 27524068
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  • id: 27524079
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  • id: 27524090
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 324, 'label': '1944.2443.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[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, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]]]}
  • id: 27524101
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  • id: 27524112
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 8, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 216, 'label': '1944.2443.1e2', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]]]}
  • id: 27524123
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 9, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 216, 'label': '1944.2443.1e3', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 4]]]}
  • id: 27523964
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 10, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 216, 'label': '1944.2443.1e4', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, -4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -4]]]}
  • id: 27523975
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 11, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 216, 'label': '1944.2443.1e5', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -2]]]}
  • id: 27523986
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 12, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 216, 'label': '1944.2443.1e6', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 2]]]}
  • id: 27523997
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  • id: 27524008
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  • id: 27524019
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 15, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.d1.a1', 'kernel_order': 108, 'label': '1944.2443.1f3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 4]]]}
  • id: 27524030
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  • id: 27524041
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  • id: 27524044
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  • id: 27524045
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  • id: 27524047
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  • id: 27524048
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  • id: 27524049
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  • id: 27524050
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  • id: 27524051
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  • id: 27524052
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  • id: 27524053
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  • id: 27524054
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  • id: 27524055
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  • id: 27524056
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  • id: 27524058
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  • id: 27524059
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  • id: 27524060
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 324, 'counter': 32, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 36, 'label': '1944.2443.2i2', 'nt': [18, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 0]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, 0]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, 4]], [[2, 2]], [[2, 2]], [[2, 4]], [[2, -2]], [[2, -1]], [[2, -4]], [[2, -2]], [[2, -1]], [[2, -4]], [[2, -4]], [[2, 1]], [[2, -1]], [[2, 4]], [[2, -2]], [[2, -4]], [[2, 2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -4]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, 4]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, 4]], [[2, -2]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, -4]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 4]], [[2, 1]], [[2, -2]], [[2, -4]], [[2, -2]], [[2, 2]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, 4]], [[2, 1]], [[2, -2]], [[2, -4]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524061
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  • id: 27524062
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  • id: 27524063
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  • id: 27524064
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  • id: 27524065
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  • id: 27524066
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  • id: 27524067
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  • id: 27524069
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  • id: 27524070
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  • id: 27524071
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  • id: 27524072
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  • id: 27524073
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  • id: 27524074
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  • id: 27524075
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  • id: 27524076
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  • id: 27524077
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  • id: 27524078
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  • id: 27524080
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  • id: 27524081
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  • id: 27524082
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  • id: 27524083
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  • id: 27524084
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  • id: 27524085
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  • id: 27524086
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  • id: 27524087
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  • id: 27524088
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  • id: 27524089
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  • id: 27524091
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  • id: 27524092
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  • id: 27524093
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  • id: 27524094
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  • id: 27524095
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 64, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 27, 'label': '1944.2443.3f2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]]]}
  • id: 27524096
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  • id: 27524097
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  • id: 27524098
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  • id: 27524099
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 68, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.d1.a1', 'kernel_order': 36, 'label': '1944.2443.3h2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[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, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]]]}
  • id: 27524100
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  • id: 27524102
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  • id: 27524103
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  • id: 27524104
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  • id: 27524105
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  • id: 27524106
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  • id: 27524107
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  • id: 27524108
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  • id: 27524109
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  • id: 27524110
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  • id: 27524111
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  • id: 27524113
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  • id: 27524114
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  • id: 27524115
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  • id: 27524116
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  • id: 27524117
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  • id: 27524118
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  • id: 27524119
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  • id: 27524120
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  • id: 27524121
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  • id: 27524122
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  • id: 27524124
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  • id: 27524125
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  • id: 27524126
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  • id: 27524127
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  • id: 27524128
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  • id: 27524129
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  • id: 27524130
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  • id: 27524131
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  • id: 27524132
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  • id: 27524133
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 99, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3s3', 'nt': [36, 304], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[3, 2]], [[3, 4]], [[3, -4]], [[3, -1]], [[3, 1]], [[3, -4]], [[3, -4]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -2]], [[3, -4]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, -2]], [[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]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 4]]]}
  • id: 27523965
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 100, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3s4', 'nt': [36, 6], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[3, -2]], [[3, -4]], [[3, 4]], [[3, 1]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 2]], [[3, 4]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, 2]], [[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]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, -2]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, -4]]]}
  • id: 27523966
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 101, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3s5', 'nt': [36, 304], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[3, -1]], [[3, -2]], [[3, 2]], [[3, -4]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, -1]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, 1]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, 1]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, -2]]]}
  • id: 27523967
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  • id: 27523968
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 103, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2443.3t1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, -4]], [[3, -2]], [[3, -4]], [[3, 2]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, 2]], [[3, 1]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -4]], [[3, 1]], [[3, 4]], [[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]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[2, 1]], [[2, 4]], [[2, -1]], [[2, -1]], [[2, 2]], [[2, 4]], [[2, -4]], [[2, 1]], [[2, -4]], [[2, 1]], [[2, -2]], [[2, -4]], [[2, 2]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, -2]], [[2, 4]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, 4]]]}
  • id: 27523969
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 104, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2443.3t2', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, 4]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, -2]], [[3, -1]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 4]], [[3, -1]], [[3, -4]], [[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]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[2, -1]], [[2, -4]], [[2, 1]], [[2, 1]], [[2, -2]], [[2, -4]], [[2, 4]], [[2, -1]], [[2, 4]], [[2, -1]], [[2, 2]], [[2, 4]], [[2, -2]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, 2]], [[2, -4]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, -4]]]}
  • id: 27523970
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 105, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2443.3t3', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, 2]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, -1]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[-1, -1]], [[-1, 4]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, -1]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[2, 4]], [[2, -2]], [[2, -4]], [[2, -4]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 4]], [[2, 2]], [[2, 4]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -1]], [[2, -4]], [[2, 1]], [[2, 1]], [[2, -2]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -2]]]}
  • id: 27523971
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 106, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2443.3t4', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, -2]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, 2]], [[3, 1]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, -2]], [[3, -4]], [[3, 2]], [[3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[-1, 1]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[2, -4]], [[2, 2]], [[2, 4]], [[2, 4]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -4]], [[2, -2]], [[2, -4]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 1]], [[2, 4]], [[2, -1]], [[2, -1]], [[2, 2]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 2]]]}
  • id: 27523972
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 107, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2443.3t5', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, -1]], [[3, 4]], [[3, -1]], [[3, -4]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, -4]], [[3, -2]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, 1]], [[3, 4]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[-1, -4]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, 4]], [[-1, 1]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, 2]], [[2, -4]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 4]], [[2, -1]], [[2, -4]], [[2, -4]], [[2, 2]], [[2, 4]], [[2, 4]], [[2, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, 1]]]}
  • id: 27523973
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  • id: 27523974
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  • id: 27523976
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 110, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3u2', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[3, 4]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, -4]], [[3, 1]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]]]}
  • id: 27523977
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 111, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3u3', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[3, 2]], [[3, 4]], [[3, -4]], [[3, -1]], [[3, 1]], [[3, -4]], [[3, -4]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -2]], [[3, -4]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, -2]], [[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]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 4]]]}
  • id: 27523978
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 112, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.89', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.2443.3u4', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[3, -2]], [[3, -4]], [[3, 4]], [[3, 1]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 2]], [[3, 4]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, 2]], [[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]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -4]]]}
  • id: 27523979
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  • id: 27523980
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  • id: 27523981
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  • id: 27523982
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  • id: 27523983
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  • id: 27523984
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  • id: 27523985
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  • id: 27523987
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  • id: 27523988
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  • id: 27523989
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  • id: 27523990
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  • id: 27523991
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  • id: 27523992
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  • id: 27523993
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  • id: 27523994
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  • id: 27523995
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  • id: 27523996
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  • id: 27523998
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  • id: 27523999
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  • id: 27524000
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  • id: 27524001
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 133, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2443.3y1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, -4]], [[3, -2]], [[3, -4]], [[3, 2]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, 2]], [[3, 1]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, -4]], [[3, 1]], [[3, 4]], [[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]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, -2]], [[3, -4]], [[3, -1]], [[3, -4]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, 2]], [[3, -1]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, -2]], [[3, -2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 4]]]}
  • id: 27524002
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 134, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2443.3y2', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, 4]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, -2]], [[3, -1]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, 4]], [[3, -1]], [[3, -4]], [[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]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, 2]], [[3, 4]], [[3, 1]], [[3, 4]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, -2]], [[3, 1]], [[3, -4]], [[3, -1]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -4]]]}
  • id: 27524003
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 135, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2443.3y3', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, 2]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, -1]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, -3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, 1]], [[3, 2]], [[3, -4]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, -1]], [[3, -4]], [[3, -2]], [[3, 4]], [[3, 2]], [[3, 1]], [[3, 1]], [[3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, -2]]]}
  • id: 27524004
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 136, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2443.3y4', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, -2]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, 2]], [[3, 1]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, -2]], [[3, -4]], [[3, 2]], [[3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, 1]], [[3, -4]], [[3, -4]], [[3, -1]], [[3, -2]], [[3, 4]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, 4]], [[3, 1]], [[3, 4]], [[3, 2]], [[3, -4]], [[3, -2]], [[3, -1]], [[3, -1]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, 2]]]}
  • id: 27524005
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  • id: 27524006
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 138, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2443.3y6', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, 1]], [[3, -4]], [[3, 1]], [[3, 4]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, 4]], [[3, 2]], [[3, -4]], [[3, -2]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, -4]], [[3, 1]], [[3, -2]], [[3, 1]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, 2]], [[3, 1]], [[3, -4]], [[3, -4]], [[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]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, -1]]]}
  • id: 27524007
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 139, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.b1', 'kernel_order': 12, 'label': '1944.2443.3z1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[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]], [[-1, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[3, -4]], [[3, 4]], [[3, 2]], [[3, 2]], [[3, 1]], [[3, -4]], [[3, -1]], [[3, -1]], [[3, 4]], [[3, -2]], [[3, 2]], [[3, -4]], [[3, -2]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 4]], [[3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[3, -4]], [[3, -2]], [[3, 4]], [[3, -2]], [[3, -1]], [[3, 2]], [[3, -4]], [[3, 1]], [[3, 2]], [[3, -1]], [[3, -1]], [[3, -4]], [[3, 4]], [[3, 1]], [[3, 2]], [[3, 1]], [[3, 4]], [[3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, -2]]]}
  • id: 27524009
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 140, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.b1', 'kernel_order': 12, 'label': '1944.2443.3z2', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[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]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[3, 4]], [[3, -4]], [[3, -2]], [[3, -2]], [[3, -1]], [[3, 4]], [[3, 1]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, -2]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[3, 4]], [[3, 2]], [[3, -4]], [[3, 2]], [[3, 1]], [[3, -2]], [[3, 4]], [[3, -1]], [[3, -2]], [[3, 1]], [[3, 1]], [[3, 4]], [[3, -4]], [[3, -1]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, -4]], [[-1, 2]]]}
  • id: 27524010
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  • id: 27524011
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  • id: 27524012
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  • id: 27524013
    {'center': '18.c1.a1', 'center_index': 18, 'center_order': 108, 'counter': 144, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '162.44', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.b1', 'kernel_order': 12, 'label': '1944.2443.3z6', 'nt': [54, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[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]], [[-1, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 4]], [[3, 4]], [[3, 2]], [[3, 1]], [[3, -2]], [[3, -2]], [[3, -1]], [[3, -4]], [[3, 4]], [[3, 1]], [[3, -4]], [[3, 2]], [[3, -2]], [[3, 2]], [[3, -1]], [[3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[3, 1]], [[3, -4]], [[3, -1]], [[3, -4]], [[3, -2]], [[3, 4]], [[3, 1]], [[3, 2]], [[3, 4]], [[3, -2]], [[3, -2]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, 4]], [[3, 2]], [[3, -1]], [[3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -4]]]}
  • id: 27524014
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 145, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '72.43', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 27, 'label': '1944.2443.6a', 'nt': [12, 44], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524015
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 146, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.164', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.2443.6b1', 'nt': [24, 564], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, -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]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524016
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 147, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.164', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.2443.6b2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 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]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524017
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 148, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.b1', 'kernel_order': 9, 'label': '1944.2443.6c1', 'nt': [36, 198], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, -1]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, -1]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524018
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  • id: 27524020
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 150, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.a1', 'kernel_order': 9, 'label': '1944.2443.6d1', 'nt': [36, 198], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 0]], [[6, 1]], [[6, 1]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524021
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 151, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.a1', 'kernel_order': 9, 'label': '1944.2443.6d2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, -1]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524022
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  • id: 27524023
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  • id: 27524024
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  • id: 27524025
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  • id: 27524026
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 156, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.562', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.2443.6f3', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, -3]], [[6, -3]], [[6, 3]], [[6, 0]], [[6, 0]], [[6, 3]], [[6, 3]], [[6, -3]], [[-3, -3]], [[-3, 3]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[6, 4]], [[6, -4]], [[6, -1]], [[6, 1]], [[6, -4]], [[6, -4]], [[6, 2]], [[6, 1]], [[6, 1]], [[6, 2]], [[6, -1]], [[6, 4]], [[6, -2]], [[6, -1]], [[6, 4]], [[6, -2]], [[6, -2]], [[-3, -4]], [[-3, 4]], [[-3, 2]], [[-3, -1]], [[-3, -2]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -4]], [[-2, -2]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -4]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 4]], [[-2, -4]], [[-2, -2]], [[-2, 4]], [[-2, 4]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524027
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 157, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.562', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.2443.6f4', 'nt': [72, 6], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 3]], [[6, 3]], [[6, -3]], [[6, 0]], [[6, 0]], [[6, -3]], [[6, -3]], [[6, 3]], [[-3, 3]], [[-3, -3]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -2]], [[6, -4]], [[6, 4]], [[6, 1]], [[6, -1]], [[6, 4]], [[6, 4]], [[6, -2]], [[6, -1]], [[6, -1]], [[6, -2]], [[6, 1]], [[6, -4]], [[6, 2]], [[6, 1]], [[6, -4]], [[6, 2]], [[6, 2]], [[-3, 4]], [[-3, -4]], [[-3, -2]], [[-3, 1]], [[-3, 2]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 2]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 4]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -4]], [[-2, 4]], [[-2, 2]], [[-2, -4]], [[-2, -4]], [[1, -4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524028
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  • id: 27524029
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  • id: 27524031
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  • id: 27524032
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  • id: 27524033
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  • id: 27524034
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  • id: 27524035
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  • id: 27524036
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  • id: 27524037
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  • id: 27524038
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 167, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.b1', 'kernel_order': 3, 'label': '1944.2443.6h2', 'nt': [108, 6], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 3]], [[6, 0]], [[6, 0]], [[6, -3]], [[6, 3]], [[6, -3]], [[6, 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]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 4]], [[6, -4]], [[6, -2]], [[6, -2]], [[6, -1]], [[6, 4]], [[6, 1]], [[6, 1]], [[6, -4]], [[6, 2]], [[6, -2]], [[6, 4]], [[6, 2]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, -4]], [[6, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 2]], [[-2, -4]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[-2, 4]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 1]], [[-2, 4]], [[-2, -4]], [[-2, -1]], [[-2, -2]], [[-2, -1]], [[-2, -4]], [[-2, 2]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -2]], [[-2, -4]], [[-2, 1]], [[-2, -4]], [[-2, 4]], [[-2, 2]], [[-2, -4]], [[-2, -2]], [[-2, 1]], [[-2, 4]], [[-2, 4]], [[-2, -1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524039
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 168, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.b1', 'kernel_order': 3, 'label': '1944.2443.6h3', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, -3]], [[6, 0]], [[6, 0]], [[6, 3]], [[6, -3]], [[6, 3]], [[6, -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]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[6, -2]], [[6, -1]], [[6, -1]], [[6, 4]], [[6, 2]], [[6, -4]], [[6, -4]], [[6, -2]], [[6, 1]], [[6, -1]], [[6, 2]], [[6, 1]], [[6, 4]], [[6, -4]], [[6, 4]], [[6, -2]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[-2, 1]], [[-2, -4]], [[-2, -1]], [[-2, 2]], [[-2, 4]], [[-2, -1]], [[-2, -4]], [[-2, -4]], [[-2, 2]], [[-2, -2]], [[-2, 4]], [[-2, -1]], [[-2, 4]], [[-2, -2]], [[-2, 1]], [[-2, 4]], [[-2, 1]], [[-2, -1]], [[-2, -4]], [[-2, -1]], [[-2, -2]], [[-2, -4]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[-2, -4]], [[-2, 2]], [[-2, 2]], [[-2, 4]], [[-2, 1]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524040
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 169, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.b1', 'kernel_order': 3, 'label': '1944.2443.6h4', 'nt': [108, 6], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 3]], [[6, 0]], [[6, 0]], [[6, -3]], [[6, 3]], [[6, -3]], [[6, 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]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -2]], [[6, 2]], [[6, 1]], [[6, 1]], [[6, -4]], [[6, -2]], [[6, 4]], [[6, 4]], [[6, 2]], [[6, -1]], [[6, 1]], [[6, -2]], [[6, -1]], [[6, -4]], [[6, 4]], [[6, -4]], [[6, 2]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, -1]], [[-2, 2]], [[-2, -1]], [[-2, 4]], [[-2, 1]], [[-2, -2]], [[-2, -4]], [[-2, 1]], [[-2, 4]], [[-2, 4]], [[-2, -2]], [[-2, 2]], [[-2, -4]], [[-2, 1]], [[-2, -4]], [[-2, 2]], [[-2, -1]], [[-2, -4]], [[-2, -1]], [[-2, 1]], [[-2, 4]], [[-2, 1]], [[-2, 2]], [[-2, 4]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[-2, 4]], [[-2, -2]], [[-2, -2]], [[-2, -4]], [[-2, -1]], [[-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27524042
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 170, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.b1', 'kernel_order': 3, 'label': '1944.2443.6h5', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, -3]], [[6, 0]], [[6, 0]], [[6, 3]], [[6, -3]], [[6, 3]], [[6, -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]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, -4]], [[6, -4]], [[6, -2]], [[6, -1]], [[6, 2]], [[6, 2]], [[6, 1]], [[6, 4]], [[6, -4]], [[6, -1]], [[6, 4]], [[6, -2]], [[6, 2]], [[6, -2]], [[6, 1]], [[6, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 4]], [[-2, 1]], [[-2, 4]], [[-2, 2]], [[-2, -4]], [[-2, -1]], [[-2, -2]], [[-2, -4]], [[-2, 2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, -4]], [[-2, -2]], [[-2, 1]], [[-2, 4]], [[-2, -2]], [[-2, 4]], [[-2, -4]], [[-2, 2]], [[-2, -4]], [[-2, 1]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, 4]], [[-2, 1]], [[-2, -4]], [[-2, 2]], [[-2, -1]], [[-2, -1]], [[-2, -2]], [[-2, 4]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27524043
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 27, 'counter': 171, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2443', 'group_counter': 2443, 'group_order': 1944, 'image': None, 'image_isoclass': '648.563', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.b1', 'kernel_order': 3, 'label': '1944.2443.6h6', 'nt': [108, 6], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 3]], [[6, 0]], [[6, 0]], [[6, -3]], [[6, 3]], [[6, -3]], [[6, 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]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, 3]], [[-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 4]], [[6, 4]], [[6, 2]], [[6, 1]], [[6, -2]], [[6, -2]], [[6, -1]], [[6, -4]], [[6, 4]], [[6, 1]], [[6, -4]], [[6, 2]], [[6, -2]], [[6, 2]], [[6, -1]], [[6, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -4]], [[-2, -1]], [[-2, -4]], [[-2, -2]], [[-2, 4]], [[-2, 1]], [[-2, 2]], [[-2, 4]], [[-2, -2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, 4]], [[-2, 2]], [[-2, -1]], [[-2, -4]], [[-2, 2]], [[-2, -4]], [[-2, 4]], [[-2, -2]], [[-2, 4]], [[-2, -1]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, -4]], [[-2, -1]], [[-2, 4]], [[-2, -2]], [[-2, 1]], [[-2, 1]], [[-2, 2]], [[-2, -4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 107435738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.2443.1.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': '1944.2443', 'subgroup_hash': 2443, 'subgroup_order': 1944, 'subgroup_tex': 'C_9\\times C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.553', 'subgroup_hash': 553, 'subgroup_order': 972, 'subgroup_tex': 'C_6^2.C_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 107435960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 27, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.572', 'subgroup_hash': 572, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '648.460', 'subgroup_hash': 460, 'subgroup_order': 648, 'subgroup_tex': 'C_6^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.556', 'subgroup_hash': 556, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.3.c1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.556', 'subgroup_hash': 556, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.3.c1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.556', 'subgroup_hash': 556, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.143', 'subgroup_hash': 143, 'subgroup_order': 486, 'subgroup_tex': '\\He_3:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 324, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.151', 'subgroup_hash': 151, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\times C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.126', 'subgroup_hash': 126, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.126', 'subgroup_hash': 126, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.6.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.126', 'subgroup_hash': 126, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.137', 'subgroup_hash': 137, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.91', 'subgroup_hash': 91, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107435805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.59', 'subgroup_hash': 59, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107435816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.52', 'subgroup_hash': 52, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.52', 'subgroup_hash': 52, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.6.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.52', 'subgroup_hash': 52, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107435850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1944.2443.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.35', 'subgroup_hash': 35, 'subgroup_order': 243, 'subgroup_tex': 'C_9\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 107435861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 27, 'characteristic': True, 'core_order': 216, 'counter': 21, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1944.2443.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 108, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '216.76', 'subgroup_hash': 76, 'subgroup_order': 216, 'subgroup_tex': 'C_{12}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 108, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.58', 'subgroup_hash': 58, 'subgroup_order': 216, 'subgroup_tex': 'D_6:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.58', 'subgroup_hash': 58, 'subgroup_order': 216, 'subgroup_tex': 'D_6:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1.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': '216.58', 'subgroup_hash': 58, 'subgroup_order': 216, 'subgroup_tex': 'D_6:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.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': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.9.f1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.89', 'subgroup_hash': 89, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 81, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.47', 'subgroup_hash': 47, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.33', 'subgroup_hash': 33, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.33', 'subgroup_hash': 33, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.33', 'subgroup_hash': 33, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.33', 'subgroup_hash': 33, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107436013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 108, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107436014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 108, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.c1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 108, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.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': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107436022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107436026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107436027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107436028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107436030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107436031
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436042
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.o1.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': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107436043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.18.p1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436053
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 81, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107436055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436057
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.24.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107436064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107436067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107436068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107436069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107436072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.d1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.d1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.d1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107435743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.f1.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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107435747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.27.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 27, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 27, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.j1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 36, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.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': '54.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 36, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.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': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.d1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.d1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 36, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.54.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.d1.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1.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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435796
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435803
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107435804
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.54.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107435806
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.54.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1.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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 107435807
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.p1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.t1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1.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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435824
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107435826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107435828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.54.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1.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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107435829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 181, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_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: 107435830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 27, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, '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: 107435831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107435832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107435833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107435834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435835
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.72.j1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.81.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.e1.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435867
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435879
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 226, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 228, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435882
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435886
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.108.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107435888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.m1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1.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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.108.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 250, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 251, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.162.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 252, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.39', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 253, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435915
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.162.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435917
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.162.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435918
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.162.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435919
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 262, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.162.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107435920
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 4, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.162.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107435930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 9, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 107435931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.89', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 89, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435932
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 9, 'counter': 274, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1944.2443.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435933
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 9, 'counter': 275, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1944.2443.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435934
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 9, 'counter': 276, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1944.2443.216.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.e1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.216.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 296, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435957
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 297, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435958
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 298, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.216.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.216.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107435962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.2443.243.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
  • id: 107435963
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435964
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435965
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 304, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435970
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435971
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 310, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 311, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435975
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 312, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 313, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.324.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107435977
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.324.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435978
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.324.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435979
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.324.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435980
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.324.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2443.486.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '486.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '486.143', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 143, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 486, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2443.486.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107435984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.486.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107435985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 3, 'counter': 321, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2443.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.563', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 563, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_3\\times C_9):S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 3, 'counter': 322, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2443.648.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.563', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 563, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_3\\times C_9):S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 3, 'counter': 323, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2443.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.562', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 562, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9\\times C_3:S_4', 'simple': True, 'solvable': True, 'special_labels': [], '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: 107435988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 3, 'counter': 324, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2443.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.572', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 572, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.f1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.648.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107435998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.972.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107435999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2443.972.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107436000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2443', 'ambient_counter': 2443, 'ambient_order': 1944, 'ambient_tex': 'C_9\\times C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 335, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.2443.1944.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1944.2443', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2443, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9\\times C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 107435738
    {'ambient': '1944.2443', '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': '72.b1.a1', 'complements': ['1944.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '3.c1.b1', '3.c1.c1', '4.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6516, 6350, 5061, 7407, 2709, 5415, 6519, 2821], 'generators': [9, 648, 108, 2, 18, 972, 162, 6], 'label': '1944.2443.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '72.43', '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': '72.43'}
  • id: 107435739
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '6.b1.a1', 'complements': ['324.l1.a1', '324.l1.b1', '324.l1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.c1.a1', '18.k1.a1', '18.o1.a1', '18.o1.b1', '18.o1.c1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5646, 2064, 7789, 2156, 3537, 4030, 8608, 8395], 'generators': [162, 6, 108, 972, 2, 648], 'label': '1944.2443.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '72.43', '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'}
  • id: 107435740
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.b1'], 'contains': ['54.p1.e1', '81.a1.b1', '81.e1.b1', '108.m1.e1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 5252, -1, 6231, -1, 2332, -1], 'generators': [9, 972, 114, 882, 162], 'label': '1944.2443.27.d1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '27.d1.e1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435741
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.c1'], 'contains': ['54.p1.f1', '81.a1.b1', '81.e1.c1', '108.m1.f1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 3590, -1, 6231, -1, 586, -1], 'generators': [9, 972, 114, 1422, 162], 'label': '1944.2443.27.d1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '27.d1.f1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435742
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.c1.a1'], 'contains': ['54.b1.a1', '54.h1.a1', '54.l1.a1', '81.b1.a1', '81.d1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3280, -1, 4709, -1, 7901, -1, 2884, -1], 'generators': [9, 648, 972, 108, 162], 'label': '1944.2443.27.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.e1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435743
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.d1.a1'], 'contains': ['54.c1.a1', '81.b1.a1', '81.e1.a1', '108.o1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1256, -1, 1229, -1, 6453, -1, 1609, -1], 'generators': [9, 972, 108, 18, 162], 'label': '1944.2443.27.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.f1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435744
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.d1.b1'], 'contains': ['54.c1.b1', '81.b1.a1', '81.e1.b1', '108.o1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1256, -1, 3407, -1, 6453, -1, 1714, -1], 'generators': [9, 972, 108, 882, 162], 'label': '1944.2443.27.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '27.f1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435745
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.d1.c1'], 'contains': ['54.c1.c1', '81.b1.a1', '81.e1.c1', '108.o1.c1'], 'core': '54.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [1256, -1, 2785, -1, 6453, -1, 691, -1], 'generators': [9, 972, 108, 1422, 162], 'label': '1944.2443.27.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '27.f1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435746
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 162, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.e1.a1', '9.e1.b1', '9.e1.c1'], 'contains': ['54.i1.a1', '54.m1.a1', '54.s1.a1', '81.c1.a1', '81.d1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4854, -1, 9953, -1, 7576, -1, 5569, -1], 'generators': [9, 648, 972, 6, 162], 'label': '1944.2443.27.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.g1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435747
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '9.f1.a1', '9.f1.b1', '9.f1.c1'], 'contains': ['54.t1.a1', '81.c1.a1', '81.e1.a1', '108.q1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2262, -1, 416, -1, 5390, -1, 3637, -1], 'generators': [9, 972, 6, 18, 162], 'label': '1944.2443.27.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.h1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435748
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.b1', '9.f1.d1', '9.f1.e1', '9.f1.f1'], 'contains': ['54.t1.b1', '81.c1.a1', '81.e1.b1', '108.q1.b1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2262, -1, 7350, -1, 5390, -1, 3395, -1], 'generators': [9, 972, 6, 882, 162], 'label': '1944.2443.27.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '27.h1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435749
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.c1', '9.f1.g1', '9.f1.h1', '9.f1.i1'], 'contains': ['54.t1.c1', '81.c1.a1', '81.e1.c1', '108.q1.c1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2262, -1, 6104, -1, 5390, -1, 3511, -1], 'generators': [9, 972, 6, 1422, 162], 'label': '1944.2443.27.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '27.h1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435750
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2592.na', 'aut_weyl_index': 3, 'centralizer': '72.b1.a1', 'complements': ['324.k1.a1', '324.l1.b1', '324.l1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.l1.a1', '18.p1.a1', '18.p1.b1', '18.p1.c1', '24.d1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6005, 5000, 1510, 6933, 2404, 1209, 5888, 5095], 'generators': [2, 972, 162, 18, 108, 6], 'label': '1944.2443.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.b1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '72.43', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435751
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.f1.a1', '18.h1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.a1.b1', '108.b1.a1', '108.b1.b1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5779, -1, 7893, -1, 7569, -1, 4449, -1], 'generators': [162, 6, 648, 108], 'label': '1944.2443.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.a1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435752
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.c1.a1', '18.e1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '108.c1.a1', '108.h1.a1', '108.h1.b1', '108.h1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8600, -1, 8796, -1, 2295, -1, 8365, -1], 'generators': [162, 2, 108, 6], 'label': '1944.2443.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435753
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.k1.a1'], 'contains': ['72.d1.a1', '108.c1.a1', '108.i1.a1', '108.i1.b1', '108.i1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7631, -1, 6774, -1, 2562, -1, 9077, -1], 'generators': [162, 650, 108, 6], 'label': '1944.2443.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '216.164', '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': '1.1'}
  • id: 107435754
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.g1.a1', '18.j1.a1', '18.o1.a1'], 'contains': ['72.i1.a1', '108.f1.a1', '108.h1.a1', '108.i1.c1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8215, -1, 9257, -1, 3096, -1, 9309, -1], 'generators': [162, 2, 648, 6], 'label': '1944.2443.36.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': '36.d1.a1', 'projective_image': '216.95', '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: 107435755
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.g1.b1', '18.j1.b1', '18.o1.b1'], 'contains': ['72.i1.b1', '108.f1.a1', '108.h1.b1', '108.i1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8215, -1, 9635, -1, 3096, -1, 8951, -1], 'generators': [162, 218, 648, 6], 'label': '1944.2443.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.b1', 'projective_image': '216.95', '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: 107435756
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.g1.c1', '18.j1.c1', '18.o1.c1'], 'contains': ['72.i1.c1', '108.f1.a1', '108.h1.c1', '108.i1.b1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8215, -1, 9446, -1, 3096, -1, 9817, -1], 'generators': [162, 110, 648, 6], 'label': '1944.2443.36.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.c1', 'projective_image': '216.95', '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: 107435757
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.o1.a1'], 'contains': ['72.i1.a1', '108.g1.a1', '108.h1.a1', '108.i1.a1', '108.i1.b1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7892, -1, 8580, -1, 2829, -1, 9563, -1], 'generators': [972, 2, 648, 6], 'label': '1944.2443.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '216.95', '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: 107435758
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.o1.b1'], 'contains': ['72.i1.b1', '108.g1.a1', '108.h1.b1', '108.i1.b1', '108.i1.c1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7892, -1, 9068, -1, 2829, -1, 9436, -1], 'generators': [972, 218, 648, 6], 'label': '1944.2443.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.e1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435759
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.o1.c1'], 'contains': ['72.i1.c1', '108.g1.a1', '108.h1.c1', '108.i1.a1', '108.i1.c1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7892, -1, 8958, -1, 2829, -1, 9943, -1], 'generators': [972, 110, 648, 6], 'label': '1944.2443.36.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.e1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435760
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.c1.b1', '12.c1.c1', '18.e1.a1'], 'contains': ['72.b1.a1', '108.j1.a1', '108.k1.a1', '108.k1.b1', '108.k1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9385, -1, 4070, -1, 1281, -1, 7642, -1], 'generators': [9, 2, 108, 6], 'label': '1944.2443.36.f1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.f1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435761
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2592.na', 'aut_weyl_index': 3, 'centralizer': '72.b1.a1', 'complements': ['324.k1.a1', '324.l1.c1', '324.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.b1'], 'contains': ['18.b1.b1', '18.c1.a1', '18.l1.b1', '18.p1.d1', '18.p1.e1', '18.p1.f1', '24.d1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6005, 5000, 6283, 5374, 2404, 1209, 5264, 6692], 'generators': [2, 972, 162, 666, 108, 6], 'label': '1944.2443.6.c1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.b1.b1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '72.43', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435762
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '18.f1.a1'], 'contains': ['72.a1.a1', '108.j1.a1', '108.l1.a1', '108.l1.b1', '108.n1.a1', '108.p1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6092, -1, 4373, -1, 5677, -1, 3915, -1], 'generators': [9, 6, 108, 648], 'label': '1944.2443.36.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.g1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435763
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['72.c1.a1', '108.j1.a1', '108.m1.a1', '108.m1.d1', '108.o1.a1', '108.q1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [987, -1, 348, -1, 3421, -1, 1729, -1], 'generators': [9, 6, 108, 18], 'label': '1944.2443.36.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '36.h1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435764
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.b1', '12.c1.b1', '12.d1.a1'], 'contains': ['72.c1.b1', '108.j1.a1', '108.m1.b1', '108.m1.e1', '108.o1.b1', '108.q1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [987, -1, 3806, -1, 3421, -1, 2206, -1], 'generators': [9, 6, 108, 882], 'label': '1944.2443.36.h1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '36.h1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435765
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.c1', '12.c1.c1', '12.d1.a1'], 'contains': ['72.c1.c1', '108.j1.a1', '108.m1.c1', '108.m1.f1', '108.o1.c1', '108.q1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [987, -1, 2772, -1, 3421, -1, 891, -1], 'generators': [9, 6, 108, 1422], 'label': '1944.2443.36.h1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '36.h1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435766
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.g1.a1'], 'contains': ['72.i1.a1', '108.k1.a1', '108.p1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9686, -1, 7108, -1, 1783, -1, 8835, -1], 'generators': [9, 2, 6, 648], 'label': '1944.2443.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.i1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435767
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.g1.b1'], 'contains': ['72.i1.b1', '108.k1.b1', '108.p1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9686, -1, 7992, -1, 1783, -1, 8607, -1], 'generators': [9, 218, 6, 648], 'label': '1944.2443.36.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.i1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435768
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.g1.c1'], 'contains': ['72.i1.c1', '108.k1.c1', '108.p1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [9686, -1, 7613, -1, 1783, -1, 9193, -1], 'generators': [9, 110, 6, 648], 'label': '1944.2443.36.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.i1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435769
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.a1', '12.c1.a1'], 'contains': ['72.j1.a1', '108.k1.a1', '108.q1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 40, -1, 96, -1, 7089, -1], 'generators': [9, 2, 6, 18], 'label': '1944.2443.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '36.j1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435770
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.b1', '12.c1.a1'], 'contains': ['72.j1.b1', '108.k1.b1', '108.q1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 131, -1, 96, -1, 6700, -1], 'generators': [9, 218, 6, 18], 'label': '1944.2443.36.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '36.j1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435771
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.c1', '12.c1.a1'], 'contains': ['72.j1.c1', '108.k1.c1', '108.q1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 223, -1, 96, -1, 7194, -1], 'generators': [9, 110, 6, 18], 'label': '1944.2443.36.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '36.j1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435806
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.j1.c1', '27.b1.c1'], 'contains': ['108.h1.c1', '162.j1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [7667, -1, 9541, -1, 4474, -1, 8013, -1], 'generators': [981, 110, 162, 6], 'label': '1944.2443.54.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.n1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435772
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2592.na', 'aut_weyl_index': 3, 'centralizer': '72.b1.a1', 'complements': ['324.k1.a1', '324.l1.a1', '324.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.c1'], 'contains': ['18.b1.c1', '18.c1.a1', '18.l1.c1', '18.p1.g1', '18.p1.h1', '18.p1.i1', '24.d1.c1'], 'core': '6.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6005, 5000, 5681, 3817, 2404, 1209, 6307, 3498], 'generators': [2, 972, 162, 1314, 108, 6], 'label': '1944.2443.6.c1.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.b1.c1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.c1', 'projective_image': '72.43', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.c1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435773
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.d1', '12.c1.b1'], 'contains': ['72.j1.d1', '108.k1.a1', '108.q1.b1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 5456, -1, 96, -1, 6190, -1], 'generators': [9, 2, 6, 882], 'label': '1944.2443.36.j1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '36.j1.d1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435774
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.e1', '12.c1.b1'], 'contains': ['72.j1.e1', '108.k1.b1', '108.q1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 6079, -1, 96, -1, 6084, -1], 'generators': [9, 218, 6, 882], 'label': '1944.2443.36.j1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '36.j1.e1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435775
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.f1', '12.c1.b1'], 'contains': ['72.j1.f1', '108.k1.c1', '108.q1.b1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 5677, -1, 96, -1, 6325, -1], 'generators': [9, 110, 6, 882], 'label': '1944.2443.36.j1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '36.j1.f1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435776
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.g1', '12.c1.c1'], 'contains': ['72.j1.g1', '108.k1.a1', '108.q1.c1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 4498, -1, 96, -1, 7404, -1], 'generators': [9, 2, 6, 1422], 'label': '1944.2443.36.j1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '36.j1.g1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435777
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.h1', '12.c1.c1'], 'contains': ['72.j1.h1', '108.k1.b1', '108.q1.c1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 4591, -1, 96, -1, 7299, -1], 'generators': [9, 218, 6, 1422], 'label': '1944.2443.36.j1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '36.j1.h1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435778
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.i1', '12.c1.c1'], 'contains': ['72.j1.i1', '108.k1.c1', '108.q1.c1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [8962, -1, 4197, -1, 96, -1, 7789, -1], 'generators': [9, 110, 6, 1422], 'label': '1944.2443.36.j1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '36.j1.i1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435779
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '12.d1.a1'], 'contains': ['72.f1.a1', '108.n1.a1', '108.o1.a1', '108.o1.b1', '108.o1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [468, -1, 1160, -1, 5110, -1, 246, -1], 'generators': [9, 18, 648, 108], 'label': '1944.2443.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107435780
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '54.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '18.c1.a1', '18.k1.a1', '18.l1.a1', '18.l1.b1', '18.l1.c1', '27.a1.a1'], 'contains': ['108.c1.a1', '162.a1.a1', '162.a1.b1', '162.b1.a1', '162.c1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3984, 5628, 4880, 6020, 6569, 4584, 3269, 4373], 'generators': [162, 972, 6, 108], 'label': '1944.2443.54.a1.a1', 'mobius_quo': -3, 'mobius_sub': 27, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.c1', '18.b1.a1', '18.b1.b1', '18.c1.a1'], 'normal_contains': ['162.b1.a1', '162.c1.a1', '162.a1.a1', '162.a1.b1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '216.164', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435781
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '54.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': ['36.j1.a1', '36.j1.c1', '36.j1.b1', '36.j1.d1', '36.j1.f1', '36.j1.e1', '36.j1.g1', '36.j1.i1', '36.j1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.d1.a1', '18.m1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '162.b1.a1', '162.l1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2587, 7529, 2989, 6673, 7901, 8363, 2693, 3749], 'generators': [162, 972, 648, 108], 'label': '1944.2443.54.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': ['18.a1.a1', '18.d1.a1'], 'normal_contains': ['162.b1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435782
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': ['36.i1.a1', '36.i1.c1', '36.i1.b1', '36.j1.d1', '36.j1.f1', '36.j1.e1', '36.j1.g1', '36.j1.i1', '36.j1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.d1.a1', '18.n1.a1', '27.f1.a1'], 'contains': ['162.b1.a1', '162.n1.a1', '216.g1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1518, 8957, 1858, 9484, 6138, 6990, 1270, 1894], 'generators': [18, 108, 162, 972], 'label': '1944.2443.54.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': ['18.b1.a1', '18.d1.a1'], 'normal_contains': ['162.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435783
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.767', 'aut_weyl_index': 18, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.g1.b1', '18.g1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7940, -1, 8847, -1, 2993, -1, 8423, -1], 'generators': [9, 648, 6, 162, 2, 108], 'label': '1944.2443.6.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': '6.d1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435784
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': ['36.i1.a1', '36.i1.c1', '36.i1.b1', '36.j1.g1', '36.j1.i1', '36.j1.h1', '36.j1.a1', '36.j1.c1', '36.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '18.d1.a1', '18.n1.b1', '27.f1.b1'], 'contains': ['162.b1.a1', '162.n1.b1', '216.g1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1518, 8957, 2406, 8483, 6138, 6990, 1375, 2920], 'generators': [666, 108, 162, 972], 'label': '1944.2443.54.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': ['18.b1.b1', '18.d1.a1'], 'normal_contains': ['162.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.c1.b1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435785
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': ['36.i1.a1', '36.i1.c1', '36.i1.b1', '36.j1.a1', '36.j1.c1', '36.j1.b1', '36.j1.d1', '36.j1.f1', '36.j1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '18.d1.a1', '18.n1.c1', '27.f1.c1'], 'contains': ['162.b1.a1', '162.n1.c1', '216.g1.c1'], 'core': '54.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1518, 8957, 2554, 7482, 6138, 6990, 718, 867], 'generators': [1314, 108, 162, 972], 'label': '1944.2443.54.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1.c1', 'normal_contained_in': ['18.b1.c1', '18.d1.a1'], 'normal_contains': ['162.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.c1.c1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.c1.c1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435786
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '54.d1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': ['36.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.o1.a1', '18.p1.a1', '18.p1.d1', '18.p1.g1', '27.b1.a1'], 'contains': ['108.h1.a1', '162.c1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6751, 3519, 7013, 3090, 4000, 1222, 6846, 5931], 'generators': [162, 972, 2, 6], 'label': '1944.2443.54.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.d1.a1', 'normal_contained_in': ['18.c1.a1'], 'normal_contains': ['162.c1.a1', '216.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '216.95', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435807
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '162.a1.a1', '162.l1.a1', '162.m1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4358, -1, 6348, -1, 9248, -1, 3823, -1], 'generators': [162, 972, 222, 648], 'label': '1944.2443.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.o1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435787
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '54.d1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': ['36.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.o1.b1', '18.p1.b1', '18.p1.e1', '18.p1.h1', '27.b1.b1'], 'contains': ['108.h1.b1', '162.c1.a1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6751, 3519, 7646, 1880, 4000, 1222, 5428, 7171], 'generators': [162, 972, 218, 6], 'label': '1944.2443.54.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.d1.b1', 'normal_contained_in': ['18.c1.a1'], 'normal_contains': ['162.c1.a1', '216.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '54.d1.b1', 'projective_image': '216.95', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435788
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '54.d1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': ['36.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.o1.c1', '18.p1.c1', '18.p1.f1', '18.p1.i1', '27.b1.c1'], 'contains': ['108.h1.c1', '162.c1.a1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6751, 3519, 7242, 4299, 4000, 1222, 6973, 8411], 'generators': [162, 972, 110, 6], 'label': '1944.2443.54.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.d1.c1', 'normal_contained_in': ['18.c1.a1'], 'normal_contains': ['162.c1.a1', '216.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '54.d1.c1', 'projective_image': '216.95', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.d1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435789
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.j1.a1', '162.d1.a1', '162.d1.b1', '162.e1.a1', '162.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7227, -1, 7833, -1, 6435, -1, 3438, -1], 'generators': [9, 162, 6, 108], 'label': '1944.2443.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.e1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435790
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.a1', '27.b1.a1'], 'contains': ['108.h1.a1', '108.k1.a1', '162.f1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8417, -1, 8337, -1, 2027, -1, 8237, -1], 'generators': [9, 162, 2, 6], 'label': '1944.2443.54.f1.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': '54.f1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435791
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.b1', '27.b1.b1'], 'contains': ['108.h1.b1', '108.k1.b1', '162.f1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8417, -1, 8584, -1, 2027, -1, 8111, -1], 'generators': [9, 162, 218, 6], 'label': '1944.2443.54.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.f1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435792
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.c1', '27.b1.c1'], 'contains': ['108.h1.c1', '108.k1.c1', '162.f1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [8417, -1, 8474, -1, 2027, -1, 8491, -1], 'generators': [9, 162, 110, 6], 'label': '1944.2443.54.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.f1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435793
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '108.l1.a1', '162.d1.a1', '162.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5642, -1, 6566, -1, 8845, -1, 4205, -1], 'generators': [9, 162, 222, 648], 'label': '1944.2443.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.g1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435794
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.767', 'aut_weyl_index': 18, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.a1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '18.j1.b1', '18.j1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7488, -1, 9147, -1, 4551, -1, 7976, -1], 'generators': [981, 648, 6, 2, 108, 162], 'label': '1944.2443.6.e1.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': '6.e1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435795
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '27.c1.b1'], 'contains': ['108.a1.b1', '108.l1.b1', '162.d1.b1', '162.g1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5642, -1, 6449, -1, 8845, -1, 4100, -1], 'generators': [9, 162, 114, 648], 'label': '1944.2443.54.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.g1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435796
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '108.n1.a1', '162.e1.a1', '162.g1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3235, -1, 5668, -1, 7194, -1, 2884, -1], 'generators': [9, 162, 108, 648], 'label': '1944.2443.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.h1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435797
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.g1.a1', '18.g1.b1', '18.g1.c1', '27.g1.a1'], 'contains': ['108.f1.a1', '108.p1.a1', '162.f1.a1', '162.g1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7053, -1, 9857, -1, 6748, -1, 5674, -1], 'generators': [9, 162, 6, 648], 'label': '1944.2443.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.i1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435798
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '162.h1.a1', '162.k1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4557, -1, 7457, -1, 9878, -1, 4575, -1], 'generators': [981, 222, 162, 648], 'label': '1944.2443.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.j1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435799
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '27.c1.b1'], 'contains': ['108.a1.b1', '162.h1.b1', '162.k1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4557, -1, 6798, -1, 9878, -1, 4323, -1], 'generators': [981, 114, 162, 648], 'label': '1944.2443.54.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.j1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435800
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.i1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '162.h1.a1', '162.h1.b1', '162.i1.a1', '162.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5014, -1, 8174, -1, 8327, -1, 3663, -1], 'generators': [981, 6, 108, 162], 'label': '1944.2443.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.k1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435801
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '162.i1.a1', '162.k1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2846, -1, 5796, -1, 9604, -1, 3535, -1], 'generators': [981, 108, 162, 648], 'label': '1944.2443.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.l1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435802
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.j1.a1', '18.j1.b1', '18.j1.c1', '27.g1.a1'], 'contains': ['108.f1.a1', '162.j1.a1', '162.k1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5277, -1, 9960, -1, 8597, -1, 5556, -1], 'generators': [981, 6, 162, 648], 'label': '1944.2443.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.m1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435803
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.j1.a1', '27.b1.a1'], 'contains': ['108.h1.a1', '162.j1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7667, -1, 9430, -1, 4474, -1, 7944, -1], 'generators': [981, 2, 162, 6], 'label': '1944.2443.54.n1.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': '54.n1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435804
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.j1.b1', '27.b1.b1'], 'contains': ['108.h1.b1', '162.j1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7667, -1, 9678, -1, 4474, -1, 7876, -1], 'generators': [981, 218, 162, 6], 'label': '1944.2443.54.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.n1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435805
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1296.2923', 'aut_weyl_index': 6, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.a1.a1', '18.l1.a1', '18.l1.b1', '18.l1.c1', '24.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6332, -1, 5119, -1, 2070, -1, 4587, -1], 'generators': [20, 972, 162, 648, 6, 108], 'label': '1944.2443.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435808
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.c1.b1'], 'contains': ['108.a1.b1', '108.b1.b1', '162.a1.b1', '162.l1.a1', '162.m1.a1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4358, -1, 6292, -1, 9248, -1, 3759, -1], 'generators': [162, 972, 114, 648], 'label': '1944.2443.54.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.o1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435809
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '27.d1.a1'], 'contains': ['162.a1.a1', '162.n1.a1', '162.o1.a1', '216.e1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 1534, -1, 5917, -1, 1616, -1], 'generators': [222, 18, 162, 972], 'label': '1944.2443.54.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.p1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435810
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '27.d1.b1'], 'contains': ['162.a1.a1', '162.n1.b1', '162.o1.b1', '216.e1.b1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 5174, -1, 5917, -1, 2093, -1], 'generators': [222, 666, 162, 972], 'label': '1944.2443.54.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '54.p1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435811
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '27.d1.c1'], 'contains': ['162.a1.a1', '162.n1.c1', '162.o1.c1', '216.e1.c1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 3579, -1, 5917, -1, 508, -1], 'generators': [222, 1314, 162, 972], 'label': '1944.2443.54.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '54.p1.c1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435812
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '27.d1.d1'], 'contains': ['162.a1.b1', '162.n1.a1', '162.o1.a1', '216.e1.d1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 1417, -1, 5917, -1, 1511, -1], 'generators': [114, 18, 162, 972], 'label': '1944.2443.54.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.p1.d1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435813
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '27.d1.e1'], 'contains': ['162.a1.b1', '162.n1.b1', '162.o1.b1', '216.e1.e1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 5083, -1, 5917, -1, 1988, -1], 'generators': [114, 666, 162, 972], 'label': '1944.2443.54.p1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '54.p1.e1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435814
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '27.d1.f1'], 'contains': ['162.a1.b1', '162.n1.c1', '162.o1.c1', '216.e1.f1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 3670, -1, 5917, -1, 372, -1], 'generators': [114, 1314, 162, 972], 'label': '1944.2443.54.p1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '54.p1.f1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435815
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.n1.a1', '18.n1.b1', '18.n1.c1'], 'contains': ['108.e1.a1', '162.b1.a1', '162.m1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3505, -1, 2480, -1, 7373, -1, 2466, -1], 'generators': [162, 972, 654, 108], 'label': '1944.2443.54.q1.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.q1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435816
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1296.3547', 'aut_weyl_index': 6, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.b1.a1', '18.k1.a1', '18.l1.b1', '18.l1.c1', '24.e1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5314, -1, 4873, -1, 1763, -1, 4875, -1], 'generators': [650, 972, 162, 18, 6, 108], 'label': '1944.2443.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435817
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.m1.a1', '18.n1.b1', '18.n1.c1'], 'contains': ['162.b1.a1', '162.o1.a1', '216.h1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2413, -1, 2105, -1, 5313, -1, 1060, -1], 'generators': [24, 108, 162, 972], 'label': '1944.2443.54.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '54.r1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435818
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '18.m1.a1', '18.n1.a1', '18.n1.c1'], 'contains': ['162.b1.a1', '162.o1.b1', '216.h1.b1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2413, -1, 2288, -1, 5313, -1, 1165, -1], 'generators': [672, 108, 162, 972], 'label': '1944.2443.54.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '54.r1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435819
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '18.m1.a1', '18.n1.a1', '18.n1.b1'], 'contains': ['162.b1.a1', '162.o1.c1', '216.h1.c1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2413, -1, 2197, -1, 5313, -1, 613, -1], 'generators': [690, 108, 162, 972], 'label': '1944.2443.54.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '54.r1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.c1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435820
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.o1.a1', '18.o1.b1', '18.o1.c1', '27.g1.a1'], 'contains': ['108.f1.a1', '108.g1.a1', '162.c1.a1', '162.l1.a1', '162.m1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4817, -1, 8959, -1, 7766, -1, 5758, -1], 'generators': [162, 972, 6, 648], 'label': '1944.2443.54.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.s1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435821
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.p1.a1', '18.p1.b1', '18.p1.c1', '27.h1.a1'], 'contains': ['162.c1.a1', '162.n1.a1', '162.o1.a1', '216.j1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2196, -1, 1272, -1, 4720, -1, 3049, -1], 'generators': [6, 18, 162, 972], 'label': '1944.2443.54.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.t1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435822
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '18.p1.d1', '18.p1.e1', '18.p1.f1', '27.h1.b1'], 'contains': ['162.c1.a1', '162.n1.b1', '162.o1.b1', '216.j1.b1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2196, -1, 7141, -1, 4720, -1, 3353, -1], 'generators': [6, 666, 162, 972], 'label': '1944.2443.54.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '54.t1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435823
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '18.p1.g1', '18.p1.h1', '18.p1.i1', '27.h1.c1'], 'contains': ['162.c1.a1', '162.n1.c1', '162.o1.c1', '216.j1.c1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2196, -1, 5498, -1, 4720, -1, 3154, -1], 'generators': [6, 1314, 162, 972], 'label': '1944.2443.54.t1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '54.t1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435824
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.o1.a1', '18.o1.b1', '18.o1.c1'], 'contains': ['108.i1.a1', '108.i1.b1', '108.i1.c1', '162.c1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6490, -1, 8695, -1, 4267, -1, 9690, -1], 'generators': [162, 972, 650, 6], 'label': '1944.2443.54.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '54.u1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435825
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.42', 'aut_weyl_index': 108, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '18.p1.a1', '18.p1.b1', '18.p1.c1'], 'contains': ['162.c1.a1', '216.l1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7505, -1, 1774, -1, 1055, -1, 5320, -1], 'generators': [20, 6, 162, 972], 'label': '1944.2443.54.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '54.v1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435826
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.42', 'aut_weyl_index': 108, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.b1', '18.p1.d1', '18.p1.e1', '18.p1.f1'], 'contains': ['162.c1.a1', '216.l1.b1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7505, -1, 6677, -1, 1055, -1, 5233, -1], 'generators': [668, 6, 162, 972], 'label': '1944.2443.54.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '54.v1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435827
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1296.3547', 'aut_weyl_index': 6, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.b1.b1', '18.k1.a1', '18.l1.a1', '18.l1.c1', '24.e1.b1'], 'core': '18.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5314, -1, 4992, -1, 1763, -1, 5014, -1], 'generators': [650, 972, 162, 666, 6, 108], 'label': '1944.2443.6.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435828
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.42', 'aut_weyl_index': 108, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.c1', '18.p1.g1', '18.p1.h1', '18.p1.i1'], 'contains': ['162.c1.a1', '216.l1.c1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7505, -1, 5969, -1, 1055, -1, 6422, -1], 'generators': [686, 6, 162, 972], 'label': '1944.2443.54.v1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.c1', 'old_label': '54.v1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435829
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.g1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.d1.a1', '216.d1.b1', '216.f1.a1', '216.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6608, 2837, 4256, 5026, 4647, 5617, 3844, 4996], 'generators': [6, 648, 108], 'label': '1944.2443.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1'], 'normal_contains': ['216.a1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '216.164', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435830
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '36.b1.a1', '36.f1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.c1.b1', '216.c1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9957, 911, 4012, 2244, 2163, 3161, 7306, 9551], 'generators': [2, 108], 'label': '1944.2443.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['18.c1.a1', '24.a1.a1'], 'normal_contains': ['216.a1.a1', '216.c1.b1', '216.c1.a1', '216.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '72.43', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.43', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435831
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '24.b1.a1', '24.d1.a1', '24.e1.a1', '36.h1.a1'], 'contains': ['216.a1.a1', '216.e1.a1', '216.e1.d1', '216.g1.a1', '216.h1.a1', '216.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [214, -1, 672, -1, 2855, -1, 1463, -1], 'generators': [6, 18, 108], 'label': '1944.2443.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435832
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '24.b1.a1', '24.d1.b1', '24.e1.b1', '36.h1.b1'], 'contains': ['216.a1.a1', '216.e1.b1', '216.e1.e1', '216.g1.b1', '216.h1.b1', '216.j1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [214, -1, 3790, -1, 2855, -1, 1939, -1], 'generators': [6, 666, 108], 'label': '1944.2443.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.c1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435833
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '24.b1.a1', '24.d1.c1', '24.e1.c1', '36.h1.c1'], 'contains': ['216.a1.a1', '216.e1.c1', '216.e1.f1', '216.g1.c1', '216.h1.c1', '216.j1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [214, -1, 2282, -1, 2855, -1, 701, -1], 'generators': [6, 1314, 108], 'label': '1944.2443.72.c1.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.c1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435834
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.e1.b1', '24.e1.c1', '36.c1.a1'], 'contains': ['216.a1.a1', '216.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9121, -1, 3093, -1, 2454, -1, 5710, -1], 'generators': [650, 108], 'label': '1944.2443.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435835
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '24.c1.a1', '24.d1.a1', '24.e1.b1', '24.e1.c1'], 'contains': ['216.a1.a1', '216.l1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8781, -1, 2691, -1, 858, -1, 5218, -1], 'generators': [20, 108], 'label': '1944.2443.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435836
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.b1', '24.c1.a1', '24.d1.b1', '24.e1.a1', '24.e1.c1'], 'contains': ['216.a1.a1', '216.l1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8781, -1, 3278, -1, 858, -1, 5112, -1], 'generators': [668, 108], 'label': '1944.2443.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435837
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.c1', '24.c1.a1', '24.d1.c1', '24.e1.a1', '24.e1.b1'], 'contains': ['216.a1.a1', '216.l1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8781, -1, 3185, -1, 858, -1, 5324, -1], 'generators': [686, 108], 'label': '1944.2443.72.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435838
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1296.3547', 'aut_weyl_index': 6, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.b1.c1', '18.k1.a1', '18.l1.a1', '18.l1.b1', '24.e1.c1'], 'core': '18.b1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5314, -1, 4686, -1, 1763, -1, 4737, -1], 'generators': [650, 972, 162, 1314, 6, 108], 'label': '1944.2443.6.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.c1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107435839
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '24.b1.a1', '36.k1.a1'], 'contains': ['216.b1.a1', '216.g1.a1', '216.g1.b1', '216.g1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [43, -1, 1225, -1, 4298, -1, 361, -1], 'generators': [18, 648], 'label': '1944.2443.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107435840
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.b1.a1'], 'contains': ['216.b1.a1', '216.h1.a1', '216.h1.b1', '216.h1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [539, -1, 1316, -1, 3674, -1, 49, -1], 'generators': [24, 648], 'label': '1944.2443.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107435841
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '24.b1.a1'], 'contains': ['216.f1.a1', '216.g1.a1', '216.h1.b1', '216.h1.c1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [399, -1, 960, -1, 3556, -1, 246, -1], 'generators': [654, 18], 'label': '1944.2443.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107435842
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.b1', '24.b1.a1'], 'contains': ['216.f1.a1', '216.g1.b1', '216.h1.a1', '216.h1.c1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [399, -1, 1444, -1, 3556, -1, 105, -1], 'generators': [654, 666], 'label': '1944.2443.72.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107435843
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.c1', '24.b1.a1'], 'contains': ['216.f1.a1', '216.g1.c1', '216.h1.a1', '216.h1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [399, -1, 1589, -1, 3556, -1, 190, -1], 'generators': [654, 1314], 'label': '1944.2443.72.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107435844
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.a1', '36.e1.a1', '36.i1.a1'], 'contains': ['216.c1.a1', '216.i1.a1', '216.k1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9738, -1, 8247, -1, 2677, -1, 8835, -1], 'generators': [2, 648], 'label': '1944.2443.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435845
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.b1', '36.e1.b1', '36.i1.b1'], 'contains': ['216.c1.b1', '216.i1.a1', '216.k1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9738, -1, 9025, -1, 2677, -1, 8721, -1], 'generators': [218, 648], 'label': '1944.2443.72.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435846
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.c1', '36.e1.c1', '36.i1.c1'], 'contains': ['216.c1.c1', '216.i1.a1', '216.k1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9738, -1, 8623, -1, 2677, -1, 9267, -1], 'generators': [110, 648], 'label': '1944.2443.72.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435847
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '24.d1.a1', '36.j1.a1'], 'contains': ['216.c1.a1', '216.j1.a1', '216.l1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 864, -1, 544, -1, 6645, -1], 'generators': [2, 18], 'label': '1944.2443.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.j1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435848
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.b1', '24.d1.a1', '36.j1.b1'], 'contains': ['216.c1.b1', '216.j1.a1', '216.l1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 1031, -1, 544, -1, 6539, -1], 'generators': [218, 18], 'label': '1944.2443.72.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.j1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435849
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '72.b1.a1', 'complements': ['972.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1', '6.c1.c1', '6.f1.a1', '6.g1.a1', '6.g1.b1', '6.g1.c1', '8.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5573, 5405, 5061, 6547, 2383, 4030, 5264, 4373], 'generators': [2, 162, 108, 18, 972, 648, 6], 'label': '1944.2443.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.a1', '6.c1.c1', '6.c1.a1', '6.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '72.43', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435850
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1944.3565', 'aut_weyl_index': 4, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '24.e1.a1', '24.e1.b1', '24.e1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8989, -1, 3758, -1, 1029, -1, 5429, -1], 'generators': [2, 18, 648], 'label': '1944.2443.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107435851
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.c1', '24.d1.a1', '36.j1.c1'], 'contains': ['216.c1.c1', '216.j1.a1', '216.l1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 746, -1, 544, -1, 6751, -1], 'generators': [110, 18], 'label': '1944.2443.72.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.j1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435852
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.d1', '24.d1.b1', '36.j1.d1'], 'contains': ['216.c1.a1', '216.j1.b1', '216.l1.b1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 5674, -1, 544, -1, 6298, -1], 'generators': [2, 666], 'label': '1944.2443.72.j1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '72.j1.d1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435853
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.e1', '24.d1.b1', '36.j1.e1'], 'contains': ['216.c1.b1', '216.j1.b1', '216.l1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 6040, -1, 544, -1, 6192, -1], 'generators': [218, 666], 'label': '1944.2443.72.j1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '72.j1.e1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435854
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.f1', '24.d1.b1', '36.j1.f1'], 'contains': ['216.c1.c1', '216.j1.b1', '216.l1.b1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 5895, -1, 544, -1, 6404, -1], 'generators': [110, 666], 'label': '1944.2443.72.j1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '72.j1.f1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435855
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.g1', '24.d1.c1', '36.j1.g1'], 'contains': ['216.c1.a1', '216.j1.c1', '216.l1.c1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 4459, -1, 544, -1, 7098, -1], 'generators': [2, 1314], 'label': '1944.2443.72.j1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '72.j1.g1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435856
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.h1', '24.d1.c1', '36.j1.h1'], 'contains': ['216.c1.b1', '216.j1.c1', '216.l1.c1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 4551, -1, 544, -1, 6947, -1], 'generators': [218, 1314], 'label': '1944.2443.72.j1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '72.j1.h1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435857
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.i1', '24.d1.c1', '36.j1.i1'], 'contains': ['216.c1.c1', '216.j1.c1', '216.l1.c1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [9399, -1, 4130, -1, 544, -1, 7499, -1], 'generators': [110, 1314], 'label': '1944.2443.72.j1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '72.j1.i1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435858
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.c1.a1', '27.d1.a1', '27.d1.b1', '27.d1.c1'], 'contains': ['162.a1.a1', '162.d1.a1', '162.h1.a1', '243.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4445, -1, 5454, -1, 9068, -1, 2778, -1], 'generators': [9, 972, 222, 162], 'label': '1944.2443.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '81.a1.a1', 'projective_image': '648.563', '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': '4.2'}
  • id: 107435859
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.c1.b1', '27.d1.d1', '27.d1.e1', '27.d1.f1'], 'contains': ['162.a1.b1', '162.d1.b1', '162.h1.b1', '243.a1.a1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4445, -1, 5182, -1, 9068, -1, 2607, -1], 'generators': [9, 972, 114, 162], 'label': '1944.2443.81.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '81.a1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107435860
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.e1.a1', '27.f1.a1', '27.f1.b1', '27.f1.c1'], 'contains': ['162.b1.a1', '162.e1.a1', '162.i1.a1', '243.a1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2920, -1, 3209, -1, 8081, -1, 2380, -1], 'generators': [9, 972, 108, 162], 'label': '1944.2443.81.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '81.b1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107435861
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.523', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': ['216.c1.a1', '216.c1.c1', '216.c1.b1', '216.l1.a1', '216.k1.a1', '216.l1.b1', '216.l1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.d1.a1', '27.e1.a1', '27.f1.a1', '27.f1.b1', '27.f1.c1', '36.k1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1012, 9089, 2067, 9484, 6028, 9005, 1609, 601], 'generators': [9, 972, 162, 18, 648, 108], 'label': '1944.2443.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '648.562', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435862
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 972, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.b1.b1', '27.b1.c1', '27.g1.a1', '27.h1.a1', '27.h1.b1', '27.h1.c1'], 'contains': ['162.c1.a1', '162.f1.a1', '162.j1.a1', '243.a1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4971, -1, 7809, -1, 6971, -1, 5135, -1], 'generators': [9, 972, 6, 162], 'label': '1944.2443.81.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '81.c1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107435863
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1.a1', '27.c1.b1', '27.e1.a1', '27.g1.a1'], 'contains': ['162.g1.a1', '162.k1.a1', '162.l1.a1', '243.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3591, -1, 6726, -1, 9391, -1, 4012, -1], 'generators': [9, 972, 162, 648], 'label': '1944.2443.81.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '81.d1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435864
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.a1', '27.d1.d1', '27.f1.a1', '27.h1.a1'], 'contains': ['162.n1.a1', '243.a1.a1', '324.l1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1284, -1, 516, -1, 6308, -1, 1848, -1], 'generators': [9, 18, 162, 972], 'label': '1944.2443.81.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '81.e1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435865
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.b1', '27.d1.e1', '27.f1.b1', '27.h1.b1'], 'contains': ['162.n1.b1', '243.a1.a1', '324.l1.b1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1284, -1, 5331, -1, 6308, -1, 2525, -1], 'generators': [9, 882, 162, 972], 'label': '1944.2443.81.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '81.e1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435866
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.c1', '27.d1.f1', '27.f1.c1', '27.h1.c1'], 'contains': ['162.n1.c1', '243.a1.a1', '324.l1.c1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1284, -1, 3486, -1, 6308, -1, 979, -1], 'generators': [9, 1422, 162, 972], 'label': '1944.2443.81.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '81.e1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435867
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.g1.a1', '54.j1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '324.a1.a1', '324.d1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6138, -1, 7570, -1, 9197, -1, 4935, -1], 'generators': [162, 222, 648], 'label': '1944.2443.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.a1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435868
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.g1.b1', '54.j1.b1', '54.o1.b1'], 'contains': ['216.d1.b1', '324.a1.b1', '324.d1.a1', '324.f1.b1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6138, -1, 6957, -1, 9197, -1, 4829, -1], 'generators': [162, 114, 648], 'label': '1944.2443.108.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.a1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435869
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '324.a1.a1', '324.e1.a1', '324.f1.b1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5676, -1, 7426, -1, 8974, -1, 4456, -1], 'generators': [972, 222, 648], 'label': '1944.2443.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.b1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435870
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.o1.b1'], 'contains': ['216.d1.b1', '324.a1.b1', '324.e1.a1', '324.f1.a1', '324.g1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5676, -1, 7333, -1, 8974, -1, 4350, -1], 'generators': [972, 114, 648], 'label': '1944.2443.108.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.b1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435871
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '54.a1.a1', '54.e1.a1', '54.k1.a1'], 'contains': ['216.a1.a1', '324.a1.a1', '324.a1.b1', '324.b1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7436, -1, 7935, -1, 6141, -1, 4244, -1], 'generators': [162, 6, 108], 'label': '1944.2443.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.c1.a1', 'projective_image': '216.164', '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: 107435872
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.195', 'aut_weyl_index': 54, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1', '3.c1.b1', '3.c1.c1'], 'contains': ['18.c1.a1', '18.e1.a1', '18.i1.a1', '27.a1.a1', '27.b1.a1', '27.b1.b1', '27.b1.c1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6798, -1, 7547, -1, 3906, -1, 7068, -1], 'generators': [9, 6, 162, 972, 2, 108], 'label': '1944.2443.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '72.43', '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': '4.2'}
  • id: 107435873
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.b1.a1', '54.h1.a1', '54.l1.a1'], 'contains': ['216.b1.a1', '324.b1.a1', '324.d1.a1', '324.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2162, -1, 6195, -1, 8751, -1, 3390, -1], 'generators': [162, 648, 108], 'label': '1944.2443.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.a1', 'projective_image': '648.562', '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: 107435874
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.q1.a1'], 'contains': ['216.f1.a1', '324.b1.a1', '324.f1.a1', '324.f1.b1', '324.g1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4424, -1, 4796, -1, 6810, -1, 3284, -1], 'generators': [162, 654, 108], 'label': '1944.2443.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.e1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435875
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '54.i1.a1', '54.m1.a1', '54.s1.a1'], 'contains': ['216.i1.a1', '324.c1.a1', '324.d1.a1', '324.g1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7157, -1, 9813, -1, 7479, -1, 5921, -1], 'generators': [162, 6, 648], 'label': '1944.2443.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435876
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.e1.a1', '36.e1.b1', '36.e1.c1', '54.s1.a1'], 'contains': ['216.i1.a1', '324.c1.a1', '324.e1.a1', '324.f1.a1', '324.f1.b1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6695, -1, 8744, -1, 7033, -1, 6027, -1], 'generators': [972, 6, 648], 'label': '1944.2443.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.g1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435877
    {'ambient': '1944.2443', 'aut_centralizer_order': 144, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.a1', '36.e1.a1', '54.d1.a1', '54.f1.a1', '54.n1.a1'], 'contains': ['216.c1.a1', '324.c1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8512, -1, 8874, -1, 2995, -1, 8142, -1], 'generators': [162, 2, 6], 'label': '1944.2443.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.h1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435878
    {'ambient': '1944.2443', 'aut_centralizer_order': 144, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.b1', '36.e1.b1', '54.d1.b1', '54.f1.b1', '54.n1.b1'], 'contains': ['216.c1.b1', '324.c1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8512, -1, 9430, -1, 2995, -1, 7927, -1], 'generators': [162, 218, 6], 'label': '1944.2443.108.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.h1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435879
    {'ambient': '1944.2443', 'aut_centralizer_order': 144, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.c1', '36.e1.c1', '54.d1.c1', '54.f1.c1', '54.n1.c1'], 'contains': ['216.c1.c1', '324.c1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8512, -1, 9251, -1, 2995, -1, 8313, -1], 'generators': [162, 110, 6], 'label': '1944.2443.108.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.h1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435880
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.b1', '36.e1.a1', '36.e1.c1', '54.u1.a1'], 'contains': ['216.k1.a1', '324.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8355, -1, 8512, -1, 3139, -1, 9043, -1], 'generators': [1134, 650, 6], 'label': '1944.2443.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.i1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435881
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.c1', '36.e1.a1', '36.e1.b1', '54.u1.a1'], 'contains': ['216.k1.a1', '324.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8355, -1, 8426, -1, 3139, -1, 9180, -1], 'generators': [972, 650, 6], 'label': '1944.2443.108.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.i1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435882
    {'ambient': '1944.2443', 'aut_centralizer_order': 72, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.a1', '36.e1.b1', '36.e1.c1', '54.u1.a1'], 'contains': ['216.k1.a1', '324.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8355, -1, 9157, -1, 3139, -1, 9111, -1], 'generators': [162, 650, 6], 'label': '1944.2443.108.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.i1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435883
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 162, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.f1.a1', '18.h1.a1', '27.a1.a1', '27.c1.a1', '27.c1.b1', '27.e1.a1', '27.g1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4447, -1, 6181, -1, 7309, -1, 3953, -1], 'generators': [9, 648, 162, 972, 6, 108], 'label': '1944.2443.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.c1.a1', 'projective_image': '216.164', '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': '12.4'}
  • id: 107435884
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.g1.a1', '36.h1.a1', '36.h1.b1', '36.h1.c1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.h1.a1', '324.h1.b1', '324.i1.a1', '324.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8115, -1, 3535, -1, 4469, -1, 2774, -1], 'generators': [9, 6, 108], 'label': '1944.2443.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.j1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435885
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.i1.a1', '36.j1.a1', '36.j1.d1', '36.j1.g1', '54.f1.a1'], 'contains': ['216.c1.a1', '324.j1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9299, -1, 5129, -1, 1849, -1, 7398, -1], 'generators': [9, 2, 6], 'label': '1944.2443.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.k1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435886
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.i1.b1', '36.j1.b1', '36.j1.e1', '36.j1.h1', '54.f1.b1'], 'contains': ['216.c1.b1', '324.j1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9299, -1, 5636, -1, 1849, -1, 7208, -1], 'generators': [9, 218, 6], 'label': '1944.2443.108.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.k1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435887
    {'ambient': '1944.2443', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.i1.c1', '36.j1.c1', '36.j1.f1', '36.j1.i1', '54.f1.c1'], 'contains': ['216.c1.c1', '324.j1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [9299, -1, 5266, -1, 1849, -1, 7614, -1], 'generators': [9, 110, 6], 'label': '1944.2443.108.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.k1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435888
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '54.g1.a1'], 'contains': ['216.d1.a1', '324.h1.a1', '324.k1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6478, -1, 5933, -1, 6364, -1, 4667, -1], 'generators': [9, 222, 648], 'label': '1944.2443.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.l1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435889
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '54.g1.b1'], 'contains': ['216.d1.b1', '324.h1.b1', '324.k1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6478, -1, 5814, -1, 6364, -1, 4562, -1], 'generators': [9, 114, 648], 'label': '1944.2443.108.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.l1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435890
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.a1', '36.h1.a1'], 'contains': ['216.e1.a1', '324.h1.a1', '324.l1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 410, -1, 3906, -1, 1769, -1], 'generators': [9, 222, 18], 'label': '1944.2443.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '108.m1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435891
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.b1', '36.h1.b1'], 'contains': ['216.e1.b1', '324.h1.a1', '324.l1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 3914, -1, 3906, -1, 2215, -1], 'generators': [9, 222, 882], 'label': '1944.2443.108.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '108.m1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435892
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.c1', '36.h1.c1'], 'contains': ['216.e1.c1', '324.h1.a1', '324.l1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 2562, -1, 3906, -1, 1101, -1], 'generators': [9, 222, 1422], 'label': '1944.2443.108.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '108.m1.c1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435893
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.d1', '36.h1.a1'], 'contains': ['216.e1.d1', '324.h1.b1', '324.l1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 318, -1, 3906, -1, 1634, -1], 'generators': [9, 114, 18], 'label': '1944.2443.108.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '108.m1.d1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435894
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 81, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.b1.a1', '27.a1.a1', '27.d1.a1', '27.d1.d1', '27.f1.a1', '27.h1.a1', '36.h1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1317, -1, 1203, -1, 5594, -1, 1971, -1], 'generators': [9, 972, 162, 6, 108, 18], 'label': '1944.2443.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.d1.a1', 'projective_image': '216.164', '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': '24.12'}
  • id: 107435895
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.e1', '36.h1.b1'], 'contains': ['216.e1.e1', '324.h1.b1', '324.l1.b1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 3822, -1, 3906, -1, 2110, -1], 'generators': [9, 114, 882], 'label': '1944.2443.108.m1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '108.m1.e1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435896
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.d1.f1', '36.h1.c1'], 'contains': ['216.e1.f1', '324.h1.b1', '324.l1.c1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [996, -1, 2653, -1, 3906, -1, 996, -1], 'generators': [9, 114, 1422], 'label': '1944.2443.108.m1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '108.m1.f1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435897
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.k1.a1', '54.h1.a1'], 'contains': ['216.b1.a1', '324.i1.a1', '324.k1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3294, -1, 3705, -1, 5577, -1, 2427, -1], 'generators': [9, 108, 648], 'label': '1944.2443.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.n1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435898
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.f1.a1', '36.h1.a1', '36.k1.a1'], 'contains': ['216.g1.a1', '324.i1.a1', '324.l1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [718, -1, 572, -1, 4128, -1, 786, -1], 'generators': [9, 108, 18], 'label': '1944.2443.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '108.o1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435899
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.f1.b1', '36.h1.b1', '36.k1.a1'], 'contains': ['216.g1.b1', '324.i1.a1', '324.l1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [718, -1, 2772, -1, 4128, -1, 891, -1], 'generators': [9, 108, 882], 'label': '1944.2443.108.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '108.o1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435900
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.f1.c1', '36.h1.c1', '36.k1.a1'], 'contains': ['216.g1.c1', '324.i1.a1', '324.l1.c1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [718, -1, 2444, -1, 4128, -1, 442, -1], 'generators': [9, 108, 1422], 'label': '1944.2443.108.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '108.o1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435901
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.i1.a1', '36.i1.b1', '36.i1.c1', '54.i1.a1'], 'contains': ['216.i1.a1', '324.j1.a1', '324.k1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7653, -1, 7791, -1, 5131, -1, 5815, -1], 'generators': [9, 6, 648], 'label': '1944.2443.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.p1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435902
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.h1.a1', '36.h1.a1', '36.j1.a1', '36.j1.b1', '36.j1.c1'], 'contains': ['216.j1.a1', '324.j1.a1', '324.l1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1762, -1, 220, -1, 3323, -1, 4033, -1], 'generators': [9, 6, 18], 'label': '1944.2443.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '108.q1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435903
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.h1.b1', '36.h1.b1', '36.j1.d1', '36.j1.e1', '36.j1.f1'], 'contains': ['216.j1.b1', '324.j1.a1', '324.l1.b1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1762, -1, 6076, -1, 3323, -1, 3928, -1], 'generators': [9, 6, 882], 'label': '1944.2443.108.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '108.q1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435904
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.h1.c1', '36.h1.c1', '36.j1.g1', '36.j1.h1', '36.j1.i1'], 'contains': ['216.j1.c1', '324.j1.a1', '324.l1.c1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1762, -1, 4367, -1, 3323, -1, 4138, -1], 'generators': [9, 6, 1422], 'label': '1944.2443.108.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '108.q1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435905
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 81, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.b1'], 'contains': ['18.b1.b1', '27.a1.a1', '27.d1.b1', '27.d1.e1', '27.f1.b1', '27.h1.b1', '36.h1.b1'], 'core': '18.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1317, -1, 5526, -1, 5594, -1, 2332, -1], 'generators': [9, 972, 162, 6, 108, 882], 'label': '1944.2443.9.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '9.d1.b1', 'projective_image': '216.164', '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': '24.12'}
  • id: 107435906
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '162.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.o1.a1', '54.p1.a1', '54.p1.b1', '54.p1.c1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 6467, 5199, 6963, 8069, 4244, 2562, 4426], 'generators': [162, 972, 222], 'label': '1944.2443.162.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': ['54.a1.a1'], 'normal_contains': ['486.a1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '648.563', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435907
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '162.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.o1.b1', '54.p1.d1', '54.p1.e1', '54.p1.f1', '81.a1.b1'], 'contains': ['324.a1.b1', '486.a1.a1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 6467, 4615, 5953, 8069, 4244, 2321, 5460], 'generators': [162, 972, 114], 'label': '1944.2443.162.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.a1.b1', 'normal_contained_in': ['54.a1.a1'], 'normal_contains': ['486.a1.a1', '648.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '162.a1.b1', 'projective_image': '648.563', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435908
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '162.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.c1.b1', '54.c1.c1', '54.q1.a1', '54.r1.a1', '54.r1.b1', '54.r1.c1', '81.b1.a1'], 'contains': ['324.b1.a1', '486.a1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2710, 8747, 2162, 8253, 7256, 6990, 1322, 2768], 'generators': [162, 972, 108], 'label': '1944.2443.162.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.b1.a1', 'normal_contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.c1', '54.c1.a1', '54.c1.b1'], 'normal_contains': ['486.a1.a1', '648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435909
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '162.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1', '54.s1.a1', '54.t1.a1', '54.t1.b1', '54.t1.c1', '54.u1.a1', '54.v1.a1', '54.v1.b1', '54.v1.c1', '81.c1.a1'], 'contains': ['324.c1.a1', '486.a1.a1'], 'core': '162.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5254, 4685, 7094, 4099, 5354, 2531, 5429, 7118], 'generators': [162, 972, 6], 'label': '1944.2443.162.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.c1.a1', 'normal_contained_in': ['54.a1.a1', '54.d1.b1', '54.d1.a1', '54.d1.c1'], 'normal_contains': ['486.a1.a1', '648.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '648.572', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435910
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.g1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.h1.a1', '486.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6343, -1, 6852, -1, 7846, -1, 3041, -1], 'generators': [9, 162, 222], 'label': '1944.2443.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.d1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435911
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.g1.b1', '81.a1.b1'], 'contains': ['324.a1.b1', '324.h1.b1', '486.b1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6343, -1, 6501, -1, 7846, -1, 2936, -1], 'generators': [9, 162, 114], 'label': '1944.2443.162.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.d1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435912
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.h1.a1', '81.b1.a1'], 'contains': ['324.b1.a1', '324.i1.a1', '486.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3531, -1, 5842, -1, 6587, -1, 2668, -1], 'generators': [9, 162, 108], 'label': '1944.2443.162.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.e1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435913
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.f1.a1', '54.f1.b1', '54.f1.c1', '54.i1.a1', '81.c1.a1'], 'contains': ['324.c1.a1', '324.j1.a1', '486.b1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7474, -1, 8194, -1, 5918, -1, 5604, -1], 'generators': [9, 162, 6], 'label': '1944.2443.162.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.f1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435914
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1.a1', '54.g1.b1', '54.h1.a1', '54.i1.a1', '81.d1.a1'], 'contains': ['324.d1.a1', '324.k1.a1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4607, -1, 6782, -1, 8240, -1, 4748, -1], 'generators': [9, 162, 648], 'label': '1944.2443.162.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '162.g1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435915
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.k1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5074, -1, 7929, -1, 9748, -1, 3477, -1], 'generators': [981, 222, 162], 'label': '1944.2443.162.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.h1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435916
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 81, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.c1'], 'contains': ['18.b1.c1', '27.a1.a1', '27.d1.c1', '27.d1.f1', '27.f1.c1', '27.h1.c1', '36.h1.c1'], 'core': '18.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [1317, -1, 4097, -1, 5594, -1, 910, -1], 'generators': [9, 972, 162, 6, 108, 1422], 'label': '1944.2443.9.d1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '9.d1.c1', 'projective_image': '216.164', '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': '24.12'}
  • id: 107435917
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.b1', '54.k1.a1', '81.a1.b1'], 'contains': ['324.a1.b1', '486.c1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5074, -1, 7500, -1, 9748, -1, 3197, -1], 'generators': [981, 114, 162], 'label': '1944.2443.162.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.h1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435918
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1.a1', '54.l1.a1', '81.b1.a1'], 'contains': ['324.b1.a1', '486.c1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3229, -1, 6425, -1, 9604, -1, 3128, -1], 'generators': [981, 108, 162], 'label': '1944.2443.162.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.i1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435919
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1.a1', '54.m1.a1', '54.n1.a1', '54.n1.b1', '54.n1.c1', '81.c1.a1'], 'contains': ['324.c1.a1', '486.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5799, -1, 8993, -1, 7663, -1, 5517, -1], 'generators': [981, 6, 162], 'label': '1944.2443.162.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.j1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435920
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.j1.b1', '54.l1.a1', '54.m1.a1', '81.d1.a1'], 'contains': ['324.d1.a1', '486.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3853, -1, 7638, -1, 9896, -1, 5023, -1], 'generators': [981, 162, 648], 'label': '1944.2443.162.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '162.k1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435921
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.o1.a1', '54.o1.b1', '54.s1.a1', '81.d1.a1'], 'contains': ['324.d1.a1', '324.e1.a1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2989, -1, 6620, -1, 9420, -1, 3759, -1], 'generators': [162, 972, 648], 'label': '1944.2443.162.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '162.l1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435922
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.o1.a1', '54.o1.b1', '54.q1.a1', '54.s1.a1'], 'contains': ['324.f1.a1', '324.f1.b1', '324.g1.a1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4895, -1, 6711, -1, 8528, -1, 3564, -1], 'generators': [162, 972, 654], 'label': '1944.2443.162.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '162.m1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435923
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.p1.a1', '54.p1.d1', '54.t1.a1', '81.e1.a1'], 'contains': ['486.a1.a1', '648.f1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1440, -1, 1769, -1, 5748, -1, 1553, -1], 'generators': [18, 162, 972], 'label': '1944.2443.162.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '162.n1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435924
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '54.p1.b1', '54.p1.e1', '54.t1.b1', '81.e1.b1'], 'contains': ['486.a1.a1', '648.f1.b1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1440, -1, 5334, -1, 5748, -1, 2029, -1], 'generators': [666, 162, 972], 'label': '1944.2443.162.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '162.n1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435925
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.c1', '54.p1.c1', '54.p1.f1', '54.t1.c1', '81.e1.c1'], 'contains': ['486.a1.a1', '648.f1.c1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1440, -1, 3192, -1, 5748, -1, 1182, -1], 'generators': [1314, 162, 972], 'label': '1944.2443.162.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '162.n1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435926
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.a1', '54.p1.d1', '54.r1.a1', '54.t1.a1'], 'contains': ['486.a1.a1', '648.g1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1902, -1, 1883, -1, 4774, -1, 1403, -1], 'generators': [24, 162, 972], 'label': '1944.2443.162.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '162.o1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435927
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.195', 'aut_weyl_index': 54, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.g1.a1', '18.j1.a1', '18.o1.a1', '27.b1.a1', '27.g1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7100, -1, 9074, -1, 4216, -1, 8136, -1], 'generators': [9, 648, 6, 972, 2, 162], 'label': '1944.2443.9.e1.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.e1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435928
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.b1', '54.p1.e1', '54.r1.b1', '54.t1.b1'], 'contains': ['486.a1.a1', '648.g1.b1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1902, -1, 4711, -1, 4774, -1, 1880, -1], 'generators': [672, 162, 972], 'label': '1944.2443.162.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '162.o1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435929
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.c1', '54.p1.f1', '54.r1.c1', '54.t1.c1'], 'contains': ['486.a1.a1', '648.g1.c1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1902, -1, 3335, -1, 4774, -1, 582, -1], 'generators': [690, 162, 972], 'label': '1944.2443.162.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.c1', 'old_label': '162.o1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107435930
    {'ambient': '1944.2443', 'aut_centralizer_order': 1944, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.c1.b1', '72.c1.c1', '72.d1.a1', '72.e1.a1', '72.e1.b1', '72.e1.c1', '108.c1.a1', '108.j1.a1'], 'contains': ['648.a1.a1', '648.a1.b1', '648.b1.a1', '648.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8001, 3047, 3340, 4648, 3629, 5617, 3760, 6289], 'generators': [6, 108], 'label': '1944.2443.216.a1.a1', 'mobius_quo': 3, 'mobius_sub': -108, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['54.a1.a1', '72.a1.a1', '72.b1.a1'], 'normal_contains': ['648.b1.a1', '648.c1.a1', '648.a1.a1', '648.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.164', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.164', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435931
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '216.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': ['9.f1.a1', '9.f1.c1', '9.f1.b1', '9.f1.d1', '9.f1.f1', '9.f1.e1', '9.f1.g1', '9.f1.i1', '9.f1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.f1.a1', '72.g1.a1', '108.d1.a1', '108.n1.a1'], 'contains': ['648.b1.a1', '648.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1483, 5721, 3583, 6384, 4875, 8363, 2091, 3597], 'generators': [648, 108], 'label': '1944.2443.216.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['54.b1.a1', '72.a1.a1'], 'normal_contains': ['648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '648.562', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.5', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435932
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '216.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.i1.a1', '72.j1.a1', '72.j1.d1', '72.j1.g1', '108.h1.a1', '108.k1.a1'], 'contains': ['648.c1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9553, 2038, 5014, 2889, 2419, 1222, 7173, 7908], 'generators': [2], 'label': '1944.2443.216.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.c1.a1', 'normal_contained_in': ['54.d1.a1', '72.b1.a1'], 'normal_contains': ['648.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '216.95', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.95', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435933
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '216.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.i1.b1', '72.j1.b1', '72.j1.e1', '72.j1.h1', '108.h1.b1', '108.k1.b1'], 'contains': ['648.c1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9553, 2038, 5681, 2044, 2419, 1222, 7070, 8456], 'generators': [218], 'label': '1944.2443.216.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.c1.b1', 'normal_contained_in': ['54.d1.b1', '72.b1.a1'], 'normal_contains': ['648.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.b1', 'projective_image': '216.95', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.95', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435934
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '216.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.i1.c1', '72.j1.c1', '72.j1.f1', '72.j1.i1', '108.h1.c1', '108.k1.c1'], 'contains': ['648.c1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9553, 2038, 5297, 3454, 2419, 1222, 7402, 9004], 'generators': [110], 'label': '1944.2443.216.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.c1.c1', 'normal_contained_in': ['54.d1.c1', '72.b1.a1'], 'normal_contains': ['648.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.c1', 'projective_image': '216.95', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.95', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435935
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.a1.a1', '108.b1.a1', '108.l1.a1'], 'contains': ['648.a1.a1', '648.d1.a1', '648.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6386, -1, 6992, -1, 6543, -1, 4340, -1], 'generators': [222, 648], 'label': '1944.2443.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435936
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.a1.b1', '108.b1.b1', '108.l1.b1'], 'contains': ['648.a1.b1', '648.d1.a1', '648.e1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6386, -1, 6544, -1, 6543, -1, 4276, -1], 'generators': [114, 648], 'label': '1944.2443.216.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.d1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435937
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.a1', '72.c1.a1', '108.m1.a1'], 'contains': ['648.a1.a1', '648.f1.a1', '648.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 617, -1, 3993, -1, 1646, -1], 'generators': [222, 18], 'label': '1944.2443.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '216.e1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435938
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.195', 'aut_weyl_index': 54, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.g1.b1', '18.j1.b1', '18.o1.b1', '27.b1.b1', '27.g1.a1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7100, -1, 9643, -1, 4216, -1, 7817, -1], 'generators': [9, 648, 6, 972, 218, 162], 'label': '1944.2443.9.e1.b1', '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.e1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435939
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.b1', '72.c1.b1', '108.m1.b1'], 'contains': ['648.a1.a1', '648.f1.b1', '648.g1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 3919, -1, 3993, -1, 1998, -1], 'generators': [222, 666], 'label': '1944.2443.216.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '216.e1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435940
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.c1', '72.c1.c1', '108.m1.c1'], 'contains': ['648.a1.a1', '648.f1.c1', '648.g1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 2464, -1, 3993, -1, 1073, -1], 'generators': [222, 1314], 'label': '1944.2443.216.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '216.e1.c1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435941
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.d1', '72.c1.a1', '108.m1.d1'], 'contains': ['648.a1.b1', '648.f1.a1', '648.g1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 735, -1, 3993, -1, 1582, -1], 'generators': [114, 18], 'label': '1944.2443.216.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '216.e1.d1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435942
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.e1', '72.c1.b1', '108.m1.e1'], 'contains': ['648.a1.b1', '648.f1.b1', '648.g1.b1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 3771, -1, 3993, -1, 1934, -1], 'generators': [114, 666], 'label': '1944.2443.216.e1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '216.e1.e1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435943
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.f1', '72.c1.c1', '108.m1.f1'], 'contains': ['648.a1.b1', '648.f1.c1', '648.g1.c1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [901, -1, 2583, -1, 3993, -1, 999, -1], 'generators': [114, 1314], 'label': '1944.2443.216.e1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '216.e1.f1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435944
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.h1.a1', '72.h1.b1', '72.h1.c1', '108.e1.a1'], 'contains': ['648.b1.a1', '648.e1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4096, -1, 2235, -1, 4741, -1, 928, -1], 'generators': [654, 108], 'label': '1944.2443.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435945
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '72.c1.a1', '72.f1.a1', '72.h1.a1', '108.o1.a1'], 'contains': ['648.b1.a1', '648.f1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [274, -1, 928, -1, 4128, -1, 786, -1], 'generators': [18, 108], 'label': '1944.2443.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.g1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435946
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '72.c1.b1', '72.f1.a1', '72.h1.b1', '108.o1.b1'], 'contains': ['648.b1.a1', '648.f1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [274, -1, 2158, -1, 4128, -1, 864, -1], 'generators': [666, 108], 'label': '1944.2443.216.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.g1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435947
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.c1', '72.c1.c1', '72.f1.a1', '72.h1.c1', '108.o1.c1'], 'contains': ['648.b1.a1', '648.f1.c1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [274, -1, 2102, -1, 4128, -1, 442, -1], 'generators': [1314, 108], 'label': '1944.2443.216.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.g1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435948
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.a1', '72.c1.a1', '72.g1.a1', '72.h1.b1', '72.h1.c1'], 'contains': ['648.b1.a1', '648.g1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1032, -1, 1456, -1, 3764, -1, 222, -1], 'generators': [24, 108], 'label': '1944.2443.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435949
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.195', 'aut_weyl_index': 54, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.g1.c1', '18.j1.c1', '18.o1.c1', '27.b1.c1', '27.g1.a1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7100, -1, 9529, -1, 4216, -1, 8265, -1], 'generators': [9, 648, 6, 972, 110, 162], 'label': '1944.2443.9.e1.c1', '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.e1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107435950
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.b1', '72.c1.b1', '72.g1.a1', '72.h1.a1', '72.h1.c1'], 'contains': ['648.b1.a1', '648.g1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1032, -1, 1998, -1, 3764, -1, 319, -1], 'generators': [672, 108], 'label': '1944.2443.216.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.h1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435951
    {'ambient': '1944.2443', 'aut_centralizer_order': 27, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.c1', '72.c1.c1', '72.g1.a1', '72.h1.a1', '72.h1.b1'], 'contains': ['648.b1.a1', '648.g1.c1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1032, -1, 1943, -1, 3764, -1, 158, -1], 'generators': [690, 108], 'label': '1944.2443.216.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.h1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107435952
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.i1.a1', '72.i1.b1', '72.i1.c1', '108.f1.a1', '108.g1.a1', '108.p1.a1'], 'contains': ['648.c1.a1', '648.d1.a1', '648.e1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6990, -1, 8472, -1, 5328, -1, 6027, -1], 'generators': [6, 648], 'label': '1944.2443.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.i1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435953
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '72.c1.a1', '72.j1.a1', '72.j1.b1', '72.j1.c1', '108.q1.a1'], 'contains': ['648.c1.a1', '648.f1.a1', '648.g1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1352, -1, 983, -1, 3465, -1, 4111, -1], 'generators': [6, 18], 'label': '1944.2443.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '216.j1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435954
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.b1', '72.c1.b1', '72.j1.d1', '72.j1.e1', '72.j1.f1', '108.q1.b1'], 'contains': ['648.c1.a1', '648.f1.b1', '648.g1.b1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1352, -1, 6130, -1, 3465, -1, 4047, -1], 'generators': [6, 666], 'label': '1944.2443.216.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '216.j1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435955
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.c1', '72.c1.c1', '72.j1.g1', '72.j1.h1', '72.j1.i1', '108.q1.c1'], 'contains': ['648.c1.a1', '648.f1.c1', '648.g1.c1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1352, -1, 4324, -1, 3465, -1, 4175, -1], 'generators': [6, 1314], 'label': '1944.2443.216.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '216.j1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435956
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.i1.a1', '72.i1.b1', '72.i1.c1', '108.i1.a1', '108.i1.b1', '108.i1.c1'], 'contains': ['648.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9151, -1, 8342, -1, 2908, -1, 8922, -1], 'generators': [650], 'label': '1944.2443.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '216.k1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435957
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.a1', '72.e1.a1', '72.j1.a1', '72.j1.b1', '72.j1.c1'], 'contains': ['648.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8989, -1, 1508, -1, 944, -1, 6393, -1], 'generators': [20], 'label': '1944.2443.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '216.l1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435958
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.b1', '72.e1.b1', '72.j1.d1', '72.j1.e1', '72.j1.f1'], 'contains': ['648.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8989, -1, 6233, -1, 944, -1, 6143, -1], 'generators': [668], 'label': '1944.2443.216.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.b1', 'old_label': '216.l1.b1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435959
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.c1', '72.e1.c1', '72.j1.g1', '72.j1.h1', '72.j1.i1'], 'contains': ['648.c1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8989, -1, 4375, -1, 944, -1, 6708, -1], 'generators': [686], 'label': '1944.2443.216.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.c1', 'old_label': '216.l1.c1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435960
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 9, 'centralizer': '72.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '9.c1.a1', '9.d1.a1', '9.d1.b1', '9.d1.c1', '12.d1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1226, 7607, 3590, 8409, 5453, 6801, 1831, 1985], 'generators': [9, 162, 108, 6, 972, 18, 648], 'label': '1944.2443.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107435961
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.p1.a1', '27.b1.a1', '27.h1.a1', '36.j1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 1105, -1, 2688, -1, 6547, -1], 'generators': [9, 972, 162, 2, 6, 18], 'label': '1944.2443.9.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.f1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435962
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '81.a1.b1', '81.b1.a1', '81.c1.a1', '81.d1.a1', '81.e1.a1', '81.e1.b1', '81.e1.c1'], 'contains': ['486.a1.a1', '486.b1.a1', '486.c1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3742, -1, 5463, -1, 8358, -1, 2855, -1], 'generators': [9, 972], 'label': '1944.2443.243.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '243.a1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107435963
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '162.a1.a1', '162.d1.a1', '162.h1.a1'], 'contains': ['648.a1.a1', '972.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6125, -1, 7554, -1, 7886, -1, 3449, -1], 'generators': [162, 222], 'label': '1944.2443.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.a1.a1', 'projective_image': '648.563', '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: 107435964
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.b1', '108.b1.b1', '108.c1.a1', '162.a1.b1', '162.d1.b1', '162.h1.b1'], 'contains': ['648.a1.b1', '972.a1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6125, -1, 6748, -1, 7886, -1, 3295, -1], 'generators': [162, 114], 'label': '1944.2443.324.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.a1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435965
    {'ambient': '1944.2443', 'aut_centralizer_order': 1296, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.d1.a1', '108.e1.a1', '162.b1.a1', '162.e1.a1', '162.i1.a1'], 'contains': ['648.b1.a1', '972.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2843, -1, 5975, -1, 7361, -1, 3055, -1], 'generators': [162, 108], 'label': '1944.2443.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.b1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435966
    {'ambient': '1944.2443', 'aut_centralizer_order': 1296, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '108.h1.b1', '108.h1.c1', '108.i1.a1', '108.i1.b1', '108.i1.c1', '162.c1.a1', '162.f1.a1', '162.j1.a1'], 'contains': ['648.c1.a1', '972.a1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7288, -1, 8653, -1, 5918, -1, 5967, -1], 'generators': [162, 6], 'label': '1944.2443.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435967
    {'ambient': '1944.2443', 'aut_centralizer_order': 1296, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.a1.b1', '108.d1.a1', '108.f1.a1', '162.g1.a1', '162.k1.a1', '162.l1.a1'], 'contains': ['648.d1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3485, -1, 6929, -1, 8496, -1, 4748, -1], 'generators': [162, 648], 'label': '1944.2443.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.d1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435968
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.b1.b1', '108.d1.a1', '108.g1.a1', '162.l1.a1'], 'contains': ['648.d1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3114, -1, 7073, -1, 8299, -1, 3988, -1], 'generators': [972, 648], 'label': '1944.2443.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '324.e1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435969
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.b1', '108.e1.a1', '108.g1.a1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5645, -1, 7277, -1, 7597, -1, 3932, -1], 'generators': [1134, 654], 'label': '1944.2443.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '324.f1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435970
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.b1', '108.b1.a1', '108.e1.a1', '108.g1.a1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5645, -1, 7148, -1, 7597, -1, 3876, -1], 'generators': [972, 654], 'label': '1944.2443.324.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '324.f1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435971
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.b1.b1', '108.e1.a1', '108.f1.a1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5760, -1, 7379, -1, 7479, -1, 3819, -1], 'generators': [162, 654], 'label': '1944.2443.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '324.g1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435972
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.p1.b1', '27.b1.b1', '27.h1.a1', '36.j1.b1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 1013, -1, 2688, -1, 6172, -1], 'generators': [9, 972, 162, 218, 6, 18], 'label': '1944.2443.9.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.f1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435973
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.a1', '108.m1.a1', '108.m1.b1', '108.m1.c1', '162.d1.a1'], 'contains': ['648.a1.a1', '972.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6423, -1, 3659, -1, 5002, -1, 2327, -1], 'generators': [9, 222], 'label': '1944.2443.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '324.h1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435974
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.b1', '108.m1.d1', '108.m1.e1', '108.m1.f1', '162.d1.b1'], 'contains': ['648.a1.b1', '972.b1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6423, -1, 3530, -1, 5002, -1, 2271, -1], 'generators': [9, 114], 'label': '1944.2443.324.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '324.h1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435975
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.n1.a1', '108.o1.a1', '108.o1.b1', '108.o1.c1', '162.e1.a1'], 'contains': ['648.b1.a1', '972.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3351, -1, 2935, -1, 4552, -1, 1167, -1], 'generators': [9, 108], 'label': '1944.2443.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '324.i1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435976
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.k1.a1', '108.k1.b1', '108.k1.c1', '108.p1.a1', '108.q1.a1', '108.q1.b1', '108.q1.c1', '162.f1.a1'], 'contains': ['648.c1.a1', '972.b1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7795, -1, 5297, -1, 4372, -1, 5604, -1], 'generators': [9, 6], 'label': '1944.2443.324.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '324.j1.a1', 'projective_image': '648.572', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435977
    {'ambient': '1944.2443', 'aut_centralizer_order': 216, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1.a1', '108.l1.b1', '108.n1.a1', '108.p1.a1', '162.g1.a1'], 'contains': ['648.d1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5468, -1, 6332, -1, 6036, -1, 4562, -1], 'generators': [9, 648], 'label': '1944.2443.324.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '324.k1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435978
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.e1.a1', '108.m1.a1', '108.m1.d1', '108.o1.a1', '108.q1.a1'], 'contains': ['648.f1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1672, -1, 400, -1, 4254, -1, 1736, -1], 'generators': [9, 18], 'label': '1944.2443.324.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '324.l1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435979
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.e1.b1', '108.m1.b1', '108.m1.e1', '108.o1.b1', '108.q1.b1'], 'contains': ['648.f1.b1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1672, -1, 4007, -1, 4254, -1, 2215, -1], 'generators': [9, 882], 'label': '1944.2443.324.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '324.l1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435980
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.e1.c1', '108.m1.c1', '108.m1.f1', '108.o1.c1', '108.q1.c1'], 'contains': ['648.f1.c1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1672, -1, 2860, -1, 4254, -1, 1223, -1], 'generators': [9, 1422], 'label': '1944.2443.324.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '324.l1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435981
    {'ambient': '1944.2443', 'aut_centralizer_order': 1296, 'aut_label': '486.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '6.b1.a1', 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.a1.b1', '162.b1.a1', '162.c1.a1', '162.l1.a1', '162.m1.a1', '162.n1.a1', '162.n1.b1', '162.n1.c1', '162.o1.a1', '162.o1.b1', '162.o1.c1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3711, 6861, 4954, 6829, 7235, 4244, 2155, 4791], 'generators': [162, 972], 'label': '1944.2443.486.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '486.a1.a1', 'normal_contained_in': ['162.b1.a1', '162.c1.a1', '162.a1.a1', '162.a1.b1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '486.a1.a1', 'projective_image': '1944.2443', 'quotient_action_image': '6.1', 'quotient_action_kernel': '81.11', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '486.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107435982
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.d1.a1', '162.d1.b1', '162.e1.a1', '162.f1.a1', '162.g1.a1', '243.a1.a1'], 'contains': ['972.a1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4711, -1, 6427, -1, 6408, -1, 3115, -1], 'generators': [9, 162], 'label': '1944.2443.486.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '486.b1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435983
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.p1.c1', '27.b1.c1', '27.h1.a1', '36.j1.c1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 921, -1, 2688, -1, 6787, -1], 'generators': [9, 972, 162, 110, 6, 18], 'label': '1944.2443.9.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.f1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435984
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.h1.a1', '162.h1.b1', '162.i1.a1', '162.j1.a1', '162.k1.a1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4527, -1, 7611, -1, 9237, -1, 3505, -1], 'generators': [981], 'label': '1944.2443.486.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '486.c1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435985
    {'ambient': '1944.2443', 'aut_centralizer_order': 1944, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.d1.a1', '216.e1.a1', '216.e1.b1', '216.e1.c1', '324.a1.a1', '324.h1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6423, 4777, 3662, 5641, 4895, 5214, 2313, 5376], 'generators': [222], 'label': '1944.2443.648.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['162.a1.a1', '216.a1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.563', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.563', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435986
    {'ambient': '1944.2443', 'aut_centralizer_order': 1944, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.d1.b1', '216.e1.d1', '216.e1.e1', '216.e1.f1', '324.a1.b1', '324.h1.b1'], 'contains': ['1944.a1.a1'], 'core': '648.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6423, 4777, 3509, 5092, 4895, 5214, 2129, 5924], 'generators': [114], 'label': '1944.2443.648.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1.b1', 'normal_contained_in': ['162.a1.b1', '216.a1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.b1', 'projective_image': '648.563', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.563', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435987
    {'ambient': '1944.2443', 'aut_centralizer_order': 3888, 'aut_label': '648.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.f1.a1', '216.g1.a1', '216.g1.b1', '216.g1.c1', '216.h1.a1', '216.h1.b1', '216.h1.c1', '324.b1.a1', '324.i1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2859, 5721, 2145, 6236, 4579, 6549, 896, 4084], 'generators': [108], 'label': '1944.2443.648.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1.a1', 'normal_contained_in': ['162.b1.a1', '216.a1.a1', '216.b1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.b1.a1', 'projective_image': '648.562', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.562', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435988
    {'ambient': '1944.2443', 'aut_centralizer_order': 3888, 'aut_label': '648.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.c1.a1', '216.c1.b1', '216.c1.c1', '216.i1.a1', '216.j1.a1', '216.j1.b1', '216.j1.c1', '216.k1.a1', '216.l1.a1', '216.l1.b1', '216.l1.c1', '324.c1.a1', '324.j1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7921, 3388, 5363, 3676, 3629, 2909, 6027, 7513], 'generators': [6], 'label': '1944.2443.648.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.c1.a1', 'normal_contained_in': ['162.c1.a1', '216.a1.a1', '216.c1.b1', '216.c1.a1', '216.c1.c1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.c1.a1', 'projective_image': '648.572', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.572', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435989
    {'ambient': '1944.2443', 'aut_centralizer_order': 1296, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.d1.a1', '216.d1.b1', '216.i1.a1', '324.d1.a1', '324.e1.a1', '324.k1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3528, -1, 6764, -1, 6036, -1, 4308, -1], 'generators': [648], 'label': '1944.2443.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.d1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435990
    {'ambient': '1944.2443', 'aut_centralizer_order': 648, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.d1.b1', '216.f1.a1', '216.i1.a1', '324.f1.a1', '324.f1.b1', '324.g1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5882, -1, 7144, -1, 5525, -1, 3904, -1], 'generators': [654], 'label': '1944.2443.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '648.e1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435991
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.n1.a1', '216.e1.a1', '216.e1.d1', '216.g1.a1', '216.j1.a1', '324.l1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1127, -1, 1563, -1, 4192, -1, 1693, -1], 'generators': [18], 'label': '1944.2443.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '648.f1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435992
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.n1.b1', '216.e1.b1', '216.e1.e1', '216.g1.b1', '216.j1.b1', '324.l1.b1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1127, -1, 4007, -1, 4192, -1, 2045, -1], 'generators': [666], 'label': '1944.2443.648.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '648.f1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435993
    {'ambient': '1944.2443', 'aut_centralizer_order': 108, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.n1.c1', '216.e1.c1', '216.e1.f1', '216.g1.c1', '216.j1.c1', '324.l1.c1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1127, -1, 2935, -1, 4192, -1, 1124, -1], 'generators': [1314], 'label': '1944.2443.648.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '648.f1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107435994
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1'], 'contains': ['18.p1.d1', '27.b1.a1', '27.h1.b1', '36.j1.d1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 6573, -1, 2688, -1, 5754, -1], 'generators': [9, 972, 162, 2, 6, 882], 'label': '1944.2443.9.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '9.f1.d1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107435995
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.o1.a1', '216.e1.a1', '216.e1.d1', '216.h1.a1', '216.j1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1371, -1, 1743, -1, 3993, -1, 1610, -1], 'generators': [24], 'label': '1944.2443.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '648.g1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435996
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.o1.b1', '216.e1.b1', '216.e1.e1', '216.h1.b1', '216.j1.b1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1371, -1, 3776, -1, 3993, -1, 1961, -1], 'generators': [672], 'label': '1944.2443.648.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.b1', 'old_label': '648.g1.b1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435997
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.o1.c1', '216.e1.c1', '216.e1.f1', '216.h1.c1', '216.j1.c1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1371, -1, 2616, -1, 3993, -1, 1034, -1], 'generators': [690], 'label': '1944.2443.648.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.c1', 'old_label': '648.g1.c1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435998
    {'ambient': '1944.2443', 'aut_centralizer_order': 2592, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7776, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.a1.b1', '324.b1.a1', '324.c1.a1', '324.d1.a1', '324.e1.a1', '324.f1.a1', '324.f1.b1', '324.g1.a1', '486.a1.a1', '486.b1.a1', '486.c1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4604, -1, 7073, -1, 7479, -1, 3505, -1], 'generators': [162], 'label': '1944.2443.972.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '486.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '972.a1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107435999
    {'ambient': '1944.2443', 'aut_centralizer_order': 432, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7776, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.h1.a1', '324.h1.b1', '324.i1.a1', '324.j1.a1', '324.k1.a1', '324.l1.a1', '324.l1.b1', '324.l1.c1', '486.b1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5076, -1, 3700, -1, 4749, -1, 2229, -1], 'generators': [9], 'label': '1944.2443.972.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '972.b1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107436000
    {'ambient': '1944.2443', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.a1.b1', '648.b1.a1', '648.c1.a1', '648.d1.a1', '648.e1.a1', '648.f1.a1', '648.f1.b1', '648.f1.c1', '648.g1.a1', '648.g1.b1', '648.g1.c1', '972.a1.a1', '972.b1.a1'], 'contains': [], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4604, 5249, 3681, 5641, 4749, 4723, 2073, 5376], 'generators': [], 'label': '1944.2443.1944.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1.a1', 'normal_contained_in': ['486.a1.a1', '648.b1.a1', '648.c1.a1', '648.a1.a1', '648.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1944.a1.a1', 'projective_image': '1944.2443', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107436001
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1'], 'contains': ['18.p1.e1', '27.b1.b1', '27.h1.b1', '36.j1.e1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 7162, -1, 2688, -1, 5649, -1], 'generators': [9, 972, 162, 218, 6, 882], 'label': '1944.2443.9.f1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '9.f1.e1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436002
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1'], 'contains': ['18.p1.f1', '27.b1.c1', '27.h1.b1', '36.j1.f1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 6739, -1, 2688, -1, 6052, -1], 'generators': [9, 972, 162, 110, 6, 882], 'label': '1944.2443.9.f1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '9.f1.f1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436003
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1'], 'contains': ['18.p1.g1', '27.b1.a1', '27.h1.c1', '36.j1.g1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 5935, -1, 2688, -1, 6682, -1], 'generators': [9, 972, 162, 2, 6, 1422], 'label': '1944.2443.9.f1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '9.f1.g1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.g1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436004
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1'], 'contains': ['18.p1.h1', '27.b1.b1', '27.h1.c1', '36.j1.h1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 6039, -1, 2688, -1, 6442, -1], 'generators': [9, 972, 162, 218, 6, 1422], 'label': '1944.2443.9.f1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '9.f1.h1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.h1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436005
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1'], 'contains': ['18.p1.i1', '27.b1.c1', '27.h1.c1', '36.j1.i1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6520, -1, 5817, -1, 2688, -1, 7203, -1], 'generators': [9, 972, 162, 110, 6, 1422], 'label': '1944.2443.9.f1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '9.f1.i1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436006
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '36.e1.a1', '36.e1.b1', '36.e1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7860, -1, 8847, -1, 2873, -1, 9199, -1], 'generators': [162, 6, 2, 648, 108], 'label': '1944.2443.12.a1.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': '12.a1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107436007
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.767', 'aut_weyl_index': 18, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.d1.a1', '6.e1.a1', '9.b1.a1', '9.c1.a1', '9.e1.a1', '9.e1.b1', '9.e1.c1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6878, -1, 8847, -1, 3906, -1, 7976, -1], 'generators': [9, 6, 162, 972, 648, 2, 108], 'label': '1944.2443.3.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': '72.43', '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': '12.4'}
  • id: 107436008
    {'ambient': '1944.2443', 'aut_centralizer_order': 6, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '36.f1.a1', '36.g1.a1', '36.i1.a1', '36.i1.b1', '36.i1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9681, -1, 4831, -1, 2016, -1, 8539, -1], 'generators': [9, 648, 2, 108, 6], 'label': '1944.2443.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.b1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436009
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.a1.a1'], 'contains': ['24.d1.a1', '36.f1.a1', '36.h1.a1', '36.j1.a1', '36.j1.b1', '36.j1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8997, -1, 289, -1, 635, -1, 6953, -1], 'generators': [9, 18, 2, 108, 6], 'label': '1944.2443.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '12.c1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436010
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1', '4.a1.a1'], 'contains': ['24.d1.b1', '36.f1.a1', '36.h1.b1', '36.j1.d1', '36.j1.e1', '36.j1.f1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8997, -1, 4387, -1, 635, -1, 6121, -1], 'generators': [9, 882, 2, 108, 6], 'label': '1944.2443.12.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.b1', 'old_label': '12.c1.b1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436011
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1', '4.a1.a1'], 'contains': ['24.d1.c1', '36.f1.a1', '36.h1.c1', '36.j1.g1', '36.j1.h1', '36.j1.i1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8997, -1, 4022, -1, 635, -1, 7312, -1], 'generators': [9, 1422, 2, 108, 6], 'label': '1944.2443.12.c1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.c1', 'old_label': '12.c1.c1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436012
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.a1.a1'], 'contains': ['24.b1.a1', '36.g1.a1', '36.h1.a1', '36.h1.b1', '36.h1.c1', '36.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [699, -1, 1383, -1, 3178, -1, 1484, -1], 'generators': [9, 108, 6, 18, 648], 'label': '1944.2443.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107436013
    {'ambient': '1944.2443', 'aut_centralizer_order': 324, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.f1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1', '54.o1.a1', '54.o1.b1', '54.q1.a1', '54.s1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4447, 5130, 5848, 5004, 7050, 7179, 3762, 5513], 'generators': [162, 108, 972, 6, 648], 'label': '1944.2443.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1'], 'normal_contains': ['54.a1.a1', '54.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '216.164', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436014
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 27, 'centralizer': '72.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.g1.a1', '9.d1.a1'], 'contains': ['54.a1.a1', '54.c1.a1', '54.p1.a1', '54.p1.d1', '54.r1.a1', '54.t1.a1', '72.c1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2521, 7188, 1674, 8483, 5151, 5201, 1827, 3133], 'generators': [6, 972, 18, 108, 162], 'label': '1944.2443.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1', '6.c1.a1'], 'normal_contains': ['54.a1.a1', '54.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107436015
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 27, 'centralizer': '72.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.b1', '6.g1.b1', '9.d1.b1'], 'contains': ['54.a1.a1', '54.c1.b1', '54.p1.b1', '54.p1.e1', '54.r1.b1', '54.t1.b1', '72.c1.b1'], 'core': '18.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2521, 7188, 5418, 7325, 5151, 5201, 2189, 4319], 'generators': [6, 972, 666, 108, 162], 'label': '1944.2443.18.b1.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.b1', 'normal_contained_in': ['6.a1.a1', '6.c1.b1'], 'normal_contains': ['54.a1.a1', '54.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107436016
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 27, 'centralizer': '72.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.c1', '6.g1.c1', '9.d1.c1'], 'contains': ['54.a1.a1', '54.c1.c1', '54.p1.c1', '54.p1.f1', '54.r1.c1', '54.t1.c1', '72.c1.c1'], 'core': '18.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2521, 7188, 4159, 6168, 5151, 5201, 910, 1947], 'generators': [6, 972, 1314, 108, 162], 'label': '1944.2443.18.b1.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.c1', 'normal_contained_in': ['6.a1.a1', '6.c1.c1'], 'normal_contains': ['54.a1.a1', '54.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.c1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107436017
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '18.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.c1.b1', '6.c1.c1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.a1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5847, 3034, 6891, 3817, 3733, 1209, 6566, 6730], 'generators': [162, 6, 972, 2, 108], 'label': '1944.2443.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.c1', '6.c1.a1', '6.c1.b1'], 'normal_contains': ['54.a1.a1', '54.d1.b1', '54.d1.a1', '54.d1.c1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '72.43', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436018
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4690', 'aut_weyl_index': 9, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '9.b1.a1', '9.d1.a1', '9.f1.a1', '9.f1.b1', '9.f1.c1', '12.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6516, -1, 1119, -1, 2709, -1, 6519, -1], 'generators': [9, 162, 18, 2, 972, 108, 6], 'label': '1944.2443.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436019
    {'ambient': '1944.2443', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.523', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': ['108.k1.a1', '108.k1.c1', '108.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['54.b1.a1', '54.c1.a1', '54.c1.b1', '54.c1.c1', '72.f1.a1'], 'core': '18.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1438, 8957, 2139, 9484, 6028, 8879, 1367, 920], 'generators': [18, 972, 648, 108, 162], 'label': '1944.2443.18.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.d1.a1', 'normal_contained_in': ['6.a1.a1', '9.a1.a1'], 'normal_contains': ['54.b1.a1', '54.c1.c1', '54.c1.a1', '54.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '648.562', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107436020
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.f1.a1', '54.e1.a1', '54.f1.a1', '54.f1.b1', '54.f1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8398, -1, 8239, -1, 2323, -1, 7691, -1], 'generators': [9, 6, 162, 2, 108], 'label': '1944.2443.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '72.43', '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': '2.1'}
  • id: 107436021
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 162, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '36.g1.a1', '54.e1.a1', '54.g1.a1', '54.g1.b1', '54.h1.a1', '54.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5286, -1, 7044, -1, 6748, -1, 4165, -1], 'generators': [9, 648, 162, 6, 108], 'label': '1944.2443.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.f1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436022
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.e1.a1'], 'contains': ['36.d1.a1', '36.i1.a1', '54.f1.a1', '54.i1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8137, -1, 9051, -1, 2590, -1, 8683, -1], 'generators': [9, 648, 162, 2, 6], 'label': '1944.2443.18.g1.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': '18.g1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436023
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.e1.b1'], 'contains': ['36.d1.b1', '36.i1.b1', '54.f1.b1', '54.i1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8137, -1, 9434, -1, 2590, -1, 8394, -1], 'generators': [9, 648, 162, 218, 6], 'label': '1944.2443.18.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436024
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.e1.c1'], 'contains': ['36.d1.c1', '36.i1.c1', '54.f1.c1', '54.i1.a1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8137, -1, 9324, -1, 2590, -1, 8937, -1], 'generators': [9, 648, 162, 110, 6], 'label': '1944.2443.18.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436025
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 162, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '54.j1.a1', '54.j1.b1', '54.k1.a1', '54.l1.a1', '54.m1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4846, -1, 7393, -1, 8327, -1, 4359, -1], 'generators': [981, 648, 6, 108, 162], 'label': '1944.2443.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436026
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.k1.a1', '54.n1.a1', '54.n1.b1', '54.n1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7194, -1, 9162, -1, 4492, -1, 7565, -1], 'generators': [981, 6, 2, 108, 162], 'label': '1944.2443.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.i1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107436027
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.e1.a1'], 'contains': ['36.d1.a1', '54.m1.a1', '54.n1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7458, -1, 9545, -1, 4762, -1, 8136, -1], 'generators': [981, 648, 2, 162, 6], 'label': '1944.2443.18.j1.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': '18.j1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436028
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.e1.b1'], 'contains': ['36.d1.b1', '54.m1.a1', '54.n1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7458, -1, 9789, -1, 4762, -1, 8006, -1], 'generators': [981, 648, 218, 162, 6], 'label': '1944.2443.18.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.j1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436029
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4690', 'aut_weyl_index': 9, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.b1', '9.b1.a1', '9.d1.b1', '9.f1.d1', '9.f1.e1', '9.f1.f1', '12.c1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6516, -1, 6382, -1, 2709, -1, 5869, -1], 'generators': [9, 162, 882, 2, 972, 108, 6], 'label': '1944.2443.3.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '3.c1.b1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436030
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.48', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.e1.c1'], 'contains': ['36.d1.c1', '54.m1.a1', '54.n1.c1'], 'core': '216.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7458, -1, 9675, -1, 4762, -1, 8265, -1], 'generators': [981, 648, 110, 162, 6], 'label': '1944.2443.18.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.j1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107436031
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.43', 'aut_weyl_index': 72, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '6.g1.b1', '6.g1.c1'], 'contains': ['36.c1.a1', '54.a1.a1', '54.u1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5585, -1, 4694, -1, 3465, -1, 7818, -1], 'generators': [162, 6, 972, 650, 108], 'label': '1944.2443.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.k1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107436032
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.745', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.g1.b1', '6.g1.c1'], 'contains': ['54.a1.a1', '54.v1.a1', '72.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6129, -1, 4968, -1, 1467, -1, 4760, -1], 'generators': [20, 972, 108, 6, 162], 'label': '1944.2443.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.l1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436033
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.745', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '6.f1.a1', '6.g1.a1', '6.g1.c1'], 'contains': ['54.a1.a1', '54.v1.b1', '72.e1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6129, -1, 5121, -1, 1467, -1, 4584, -1], 'generators': [668, 972, 108, 6, 162], 'label': '1944.2443.18.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.l1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436034
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.745', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '6.f1.a1', '6.g1.a1', '6.g1.b1'], 'contains': ['54.a1.a1', '54.v1.c1', '72.e1.c1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6129, -1, 5249, -1, 1467, -1, 4936, -1], 'generators': [686, 972, 108, 6, 162], 'label': '1944.2443.18.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.l1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.c1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436035
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.523', 'aut_weyl_index': 18, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['54.b1.a1', '54.r1.a1', '54.r1.b1', '54.r1.c1', '72.g1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2933, -1, 2320, -1, 5843, -1, 1015, -1], 'generators': [24, 972, 648, 108, 162], 'label': '1944.2443.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.m1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436036
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['54.c1.a1', '54.q1.a1', '54.r1.b1', '54.r1.c1', '72.h1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2752, -1, 1823, -1, 5658, -1, 1279, -1], 'generators': [654, 972, 18, 108, 162], 'label': '1944.2443.18.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436037
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['54.c1.b1', '54.q1.a1', '54.r1.a1', '54.r1.c1', '72.h1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2752, -1, 2243, -1, 5658, -1, 1103, -1], 'generators': [654, 972, 666, 108, 162], 'label': '1944.2443.18.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.n1.b1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436038
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['54.c1.c1', '54.q1.a1', '54.r1.a1', '54.r1.b1', '72.h1.c1'], 'core': '54.c1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2752, -1, 2474, -1, 5658, -1, 1191, -1], 'generators': [654, 972, 1314, 108, 162], 'label': '1944.2443.18.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.n1.c1', 'projective_image': '648.562', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.c1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107436039
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.e1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '54.d1.a1', '54.s1.a1', '54.u1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6748, -1, 8509, -1, 4000, -1, 9064, -1], 'generators': [162, 6, 972, 2, 648], 'label': '1944.2443.18.o1.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.o1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107436040
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4690', 'aut_weyl_index': 9, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.c1', '9.b1.a1', '9.d1.c1', '9.f1.g1', '9.f1.h1', '9.f1.i1', '12.c1.c1'], 'core': '6.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6516, -1, 5746, -1, 2709, -1, 6682, -1], 'generators': [9, 162, 1422, 2, 972, 108, 6], 'label': '1944.2443.3.c1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '3.c1.c1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436041
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.e1.b1'], 'contains': ['36.d1.b1', '36.e1.b1', '54.d1.b1', '54.s1.a1', '54.u1.a1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6748, -1, 8779, -1, 4000, -1, 8811, -1], 'generators': [162, 6, 972, 218, 648], 'label': '1944.2443.18.o1.b1', '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.o1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107436042
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.e1.c1'], 'contains': ['36.d1.c1', '36.e1.c1', '54.d1.c1', '54.s1.a1', '54.u1.a1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6748, -1, 8620, -1, 4000, -1, 9335, -1], 'generators': [162, 6, 972, 110, 648], 'label': '1944.2443.18.o1.c1', '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.o1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107436043
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.f1.a1'], 'contains': ['54.d1.a1', '54.t1.a1', '54.v1.a1', '72.j1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 1576, -1, 1732, -1, 5882, -1], 'generators': [2, 972, 18, 6, 162], 'label': '1944.2443.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.p1.a1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436044
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.f1.b1'], 'contains': ['54.d1.b1', '54.t1.a1', '54.v1.a1', '72.j1.b1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 1484, -1, 1732, -1, 5302, -1], 'generators': [218, 972, 18, 6, 162], 'label': '1944.2443.18.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.p1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436045
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.f1.c1'], 'contains': ['54.d1.c1', '54.t1.a1', '54.v1.a1', '72.j1.c1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 1340, -1, 1732, -1, 5986, -1], 'generators': [110, 972, 18, 6, 162], 'label': '1944.2443.18.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.p1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436046
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.f1.d1'], 'contains': ['54.d1.a1', '54.t1.b1', '54.v1.b1', '72.j1.d1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 6528, -1, 1732, -1, 5197, -1], 'generators': [2, 972, 666, 6, 162], 'label': '1944.2443.18.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '18.p1.d1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436047
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.f1.e1'], 'contains': ['54.d1.b1', '54.t1.b1', '54.v1.b1', '72.j1.e1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 7162, -1, 1732, -1, 5092, -1], 'generators': [218, 972, 666, 6, 162], 'label': '1944.2443.18.p1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '18.p1.e1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436048
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.f1.f1'], 'contains': ['54.d1.c1', '54.t1.b1', '54.v1.b1', '72.j1.f1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 6739, -1, 1732, -1, 5716, -1], 'generators': [110, 972, 666, 6, 162], 'label': '1944.2443.18.p1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '18.p1.f1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436049
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '9.f1.g1'], 'contains': ['54.d1.a1', '54.t1.c1', '54.v1.c1', '72.j1.g1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 5947, -1, 1732, -1, 6450, -1], 'generators': [2, 972, 1314, 6, 162], 'label': '1944.2443.18.p1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '18.p1.g1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.g1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436050
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '9.f1.h1'], 'contains': ['54.d1.b1', '54.t1.c1', '54.v1.c1', '72.j1.h1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 6039, -1, 1732, -1, 6315, -1], 'generators': [218, 972, 1314, 6, 162], 'label': '1944.2443.18.p1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '18.p1.h1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.h1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436051
    {'ambient': '1944.2443', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1944.3565', 'aut_weyl_index': 4, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '12.c1.a1', '12.c1.b1', '12.c1.c1', '12.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9044, -1, 3904, -1, 1467, -1, 6912, -1], 'generators': [9, 108, 648, 2, 6, 18], 'label': '1944.2443.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107436052
    {'ambient': '1944.2443', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.188', 'aut_weyl_index': 54, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '9.f1.i1'], 'contains': ['54.d1.c1', '54.t1.c1', '54.v1.c1', '72.j1.i1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6509, -1, 5749, -1, 1732, -1, 6682, -1], 'generators': [110, 972, 1314, 6, 162], 'label': '1944.2443.18.p1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '18.p1.i1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436053
    {'ambient': '1944.2443', 'aut_centralizer_order': 36, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '6.b1.a1', 'complements': ['81.e1.a1', '81.e1.b1', '81.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '72.i1.a1', '72.i1.b1', '72.i1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9877, 911, 4738, 516, 1544, 3224, 8721, 8395], 'generators': [2, 648, 108], 'label': '1944.2443.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.b1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '72.43', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436054
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '8.a1.a1', '12.d1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.c1.b1', '72.c1.c1', '72.f1.a1', '72.g1.a1', '72.h1.a1', '72.h1.b1', '72.h1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [368, -1, 989, -1, 3708, -1, 68, -1], 'generators': [6, 18, 648], 'label': '1944.2443.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107436055
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.117', 'aut_weyl_index': 24, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '8.a1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.e1.b1', '72.e1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7621, -1, 3529, -1, 806, -1, 4714, -1], 'generators': [20, 648], 'label': '1944.2443.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107436056
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.a1.a1', '12.c1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.e1.a1', '72.j1.a1', '72.j1.b1', '72.j1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9501, -1, 1108, -1, 399, -1, 6526, -1], 'generators': [2, 18, 108], 'label': '1944.2443.24.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436057
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '8.a1.a1', '12.c1.b1'], 'contains': ['72.b1.a1', '72.c1.b1', '72.e1.b1', '72.j1.d1', '72.j1.e1', '72.j1.f1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9501, -1, 4211, -1, 399, -1, 5911, -1], 'generators': [2, 666, 108], 'label': '1944.2443.24.d1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436058
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.170', 'aut_weyl_index': 36, 'centralizer': '24.d1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '8.a1.a1', '12.c1.c1'], 'contains': ['72.b1.a1', '72.c1.c1', '72.e1.c1', '72.j1.g1', '72.j1.h1', '72.j1.i1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9501, -1, 3861, -1, 399, -1, 7518, -1], 'generators': [2, 1314, 108], 'label': '1944.2443.24.d1.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.d1.c1', 'projective_image': '72.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107436059
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '108.38', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '8.a1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.e1.b1', '72.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8742, -1, 3070, -1, 621, -1, 4920, -1], 'generators': [650, 18], 'label': '1944.2443.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107436060
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '108.38', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.b1', '8.a1.a1'], 'contains': ['72.c1.b1', '72.d1.a1', '72.e1.a1', '72.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8742, -1, 3435, -1, 621, -1, 5038, -1], 'generators': [650, 666], 'label': '1944.2443.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107436061
    {'ambient': '1944.2443', 'aut_centralizer_order': 3, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '108.38', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.c1', '8.a1.a1'], 'contains': ['72.c1.c1', '72.d1.a1', '72.e1.a1', '72.e1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8742, -1, 1933, -1, 621, -1, 4801, -1], 'generators': [650, 1314], 'label': '1944.2443.24.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.c1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107436062
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 9, 'centralizer': '72.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '18.d1.a1', '18.m1.a1', '18.n1.a1', '18.n1.b1', '18.n1.c1', '24.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3081, 7607, 3160, 8409, 5312, 6713, 1323, 1985], 'generators': [6, 972, 162, 18, 648, 108], 'label': '1944.2443.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['18.a1.a1', '18.b1.c1', '18.b1.a1', '18.b1.b1', '18.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107436063
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 486, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.c1.a1', '9.d1.a1', '9.d1.b1', '9.d1.c1'], 'contains': ['54.a1.a1', '54.e1.a1', '54.k1.a1', '81.a1.a1', '81.a1.b1', '81.b1.a1', '81.c1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3783, -1, 5727, -1, 7309, -1, 3125, -1], 'generators': [9, 162, 972, 6, 108], 'label': '1944.2443.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '27.a1.a1', 'projective_image': '216.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107436064
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.e1.a1', '9.f1.a1', '9.f1.d1', '9.f1.g1'], 'contains': ['54.d1.a1', '54.f1.a1', '54.n1.a1', '81.c1.a1'], 'core': '54.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6955, -1, 7547, -1, 4246, -1, 7118, -1], 'generators': [9, 6, 972, 2, 162], 'label': '1944.2443.27.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': '27.b1.a1', 'projective_image': '216.95', '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': '4.2'}
  • id: 107436065
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.e1.b1', '9.f1.b1', '9.f1.e1', '9.f1.h1'], 'contains': ['54.d1.b1', '54.f1.b1', '54.n1.b1', '81.c1.a1'], 'core': '54.d1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6955, -1, 7779, -1, 4246, -1, 6788, -1], 'generators': [9, 6, 972, 218, 162], 'label': '1944.2443.27.b1.b1', '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.b1.b1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107436066
    {'ambient': '1944.2443', 'aut_centralizer_order': 12, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.15', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.e1.c1', '9.f1.c1', '9.f1.f1', '9.f1.i1'], 'contains': ['54.d1.c1', '54.f1.c1', '54.n1.c1', '81.c1.a1'], 'core': '54.d1.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6955, -1, 7650, -1, 4246, -1, 7448, -1], 'generators': [9, 6, 972, 110, 162], 'label': '1944.2443.27.b1.c1', '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.b1.c1', 'projective_image': '216.95', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107436067
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1'], 'contains': ['54.g1.a1', '54.j1.a1', '54.o1.a1', '81.a1.a1', '81.d1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4287, -1, 6525, -1, 9158, -1, 4018, -1], 'generators': [9, 648, 972, 222, 162], 'label': '1944.2443.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.c1.a1', 'projective_image': '648.563', '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': '12.4'}
  • id: 107436068
    {'ambient': '1944.2443', 'aut_centralizer_order': 54, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1'], 'contains': ['54.g1.b1', '54.j1.b1', '54.o1.b1', '81.a1.b1', '81.d1.a1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4287, -1, 6387, -1, 9158, -1, 3888, -1], 'generators': [9, 648, 972, 114, 162], 'label': '1944.2443.27.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.c1.b1', 'projective_image': '648.563', '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': '12.4'}
  • id: 107436069
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1'], 'contains': ['54.p1.a1', '81.a1.a1', '81.e1.a1', '108.m1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 651, -1, 6231, -1, 2076, -1], 'generators': [9, 972, 222, 18, 162], 'label': '1944.2443.27.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.d1.a1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436070
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.b1'], 'contains': ['54.p1.b1', '81.a1.a1', '81.e1.b1', '108.m1.b1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 5343, -1, 6231, -1, 2438, -1], 'generators': [9, 972, 222, 882, 162], 'label': '1944.2443.27.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '27.d1.b1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436071
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.c1'], 'contains': ['54.p1.c1', '81.a1.a1', '81.e1.c1', '108.m1.c1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 3499, -1, 6231, -1, 796, -1], 'generators': [9, 972, 222, 1422, 162], 'label': '1944.2443.27.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '27.d1.c1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107436072
    {'ambient': '1944.2443', 'aut_centralizer_order': 9, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 162, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1'], 'contains': ['54.p1.d1', '81.a1.b1', '81.e1.a1', '108.m1.d1'], 'core': '162.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1472, -1, 560, -1, 6231, -1, 1971, -1], 'generators': [9, 972, 114, 18, 162], 'label': '1944.2443.27.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.d1.d1', 'projective_image': '648.563', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}