Abstract group data - 2160.dm

Formats: - HTML - YAML - JSON - 2025-11-15T08:05:50.036386

• 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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [4, 12, 6, 24, 4], 'aut_gens': [[288206, 48, 288183, 160649, 13455751025, 10110, 5094, 288152], [160679, 30, 338600, 328479, 13455918873, 298281, 116639, 160625], [288158, 48, 328502, 45359, 7743904505, 5790, 5046, 288152], [328479, 48, 288183, 44638, 25866130984, 5790, 5046, 328473], [155590, 48, 298263, 55, 13455590401, 338582, 45311, 155584], [160679, 48, 338582, 328497, 13455918873, 298263, 116639, 160625]], 'aut_group': None, 'aut_hash': 7882798221068001515, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 19, 'aut_perms': [97623060562171011, 83673582473787954, 89387170365081612, 27838675343844895, 97518440353051011], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 2, 1], [2, 9, 1, 1], [2, 18, 2, 1], [2, 27, 1, 1], [3, 2, 1, 1], [3, 4, 2, 1], [3, 8, 2, 1], [4, 18, 1, 1], [4, 54, 1, 1], [5, 1, 4, 1], [6, 12, 2, 3], [6, 18, 1, 1], [6, 24, 2, 1], [6, 36, 2, 1], [10, 3, 4, 1], [10, 6, 8, 1], [10, 9, 4, 1], [10, 18, 8, 1], [10, 27, 4, 1], [12, 36, 1, 1], [15, 2, 4, 1], [15, 4, 8, 1], [15, 8, 8, 1], [20, 18, 4, 1], [20, 54, 4, 1], [30, 12, 8, 3], [30, 18, 4, 1], [30, 24, 8, 1], [30, 36, 8, 1], [60, 36, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_6\\times S_3\\wr C_2).C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.4662', 'autcentquo_hash': 4662, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 6, 2], [2, 9, 1], [2, 18, 2], [2, 27, 1], [3, 2, 1], [3, 4, 2], [3, 8, 2], [4, 18, 1], [4, 54, 1], [5, 1, 4], [6, 12, 6], [6, 18, 1], [6, 24, 2], [6, 36, 2], [10, 3, 4], [10, 6, 8], [10, 9, 4], [10, 18, 8], [10, 27, 4], [12, 36, 1], [15, 2, 4], [15, 4, 8], [15, 8, 8], [20, 18, 4], [20, 54, 4], [30, 12, 24], [30, 18, 4], [30, 24, 8], [30, 36, 8], [60, 36, 4]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '432.741', 'commutator_count': 1, 'commutator_label': '54.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 91, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['6.1', 1], ['72.40', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 9, 1, 1], [2, 18, 1, 2], [2, 27, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 8, 1, 2], [4, 18, 1, 1], [4, 54, 1, 1], [5, 1, 4, 1], [6, 12, 1, 6], [6, 18, 1, 1], [6, 24, 1, 2], [6, 36, 1, 2], [10, 3, 4, 1], [10, 6, 4, 2], [10, 9, 4, 1], [10, 18, 4, 2], [10, 27, 4, 1], [12, 36, 1, 1], [15, 2, 4, 1], [15, 4, 4, 2], [15, 8, 4, 2], [20, 18, 4, 1], [20, 54, 4, 1], [30, 12, 4, 6], [30, 18, 4, 1], [30, 24, 4, 2], [30, 36, 4, 2], [60, 36, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 833280, 'exponent': 60, 'exponents_of_order': [4, 3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 0, 16]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2160.dm', 'hash': 5240928682237879649, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 3, 2, 2, 3, 2, 2], 'inner_gens': [[288206, 30, 328520, 116591, 13455706985, 10128, 5094, 288152], [288158, 48, 288183, 160679, 13455751025, 10110, 5046, 288152], [25, 48, 288183, 45311, 13455635705, 10110, 5064, 1], [726, 30, 10128, 160649, 13455751025, 288201, 7, 720], [774, 48, 10110, 160649, 13455751025, 288183, 55, 720], [288176, 48, 288183, 111550, 13455701944, 10110, 10824, 288152], [288206, 30, 288201, 155590, 13455745984, 5808, 5094, 288152], [288206, 48, 328502, 116609, 13455706985, 10110, 5094, 288152]], 'inner_hash': 741, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': False, 'inner_tex': 'S_3^3:C_2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 16, 'irrep_stats': [[1, 40], [2, 30], [4, 45], [8, 20]], 'label': '2160.dm', 'linC_count': 768, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 256, 'linQ_dim': 10, 'linQ_dim_count': 256, 'linR_count': 576, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'S3^3:C10', '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 135, 'number_divisions': 54, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 236, 'number_subgroup_classes': 384, 'number_subgroups': 3440, 'old_label': None, 'order': 2160, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 87], [3, 26], [4, 72], [5, 4], [6, 210], [10, 348], [12, 36], [15, 104], [20, 288], [30, 840], [60, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [288872, 0], 'outer_gens': [[160679, 48, 293943, 288176, 25866374552, 334262, 44638, 160625], [288206, 48, 328502, 160649, 7744019825, 5790, 10854, 288152]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 17], [8, 10], [16, 9], [32, 4]], 'representations': {'PC': {'code': '50237945519281595157768678547456823850464971197908070564677', 'gens': [1, 2, 5, 6, 8], 'pres': [8, 2, 2, 2, 5, 3, 2, 3, 3, 353, 41, 66, 10412, 820, 30725, 15373, 7221, 141, 31366, 15694, 6742, 92167, 815]}, 'Perm': {'d': 14, 'gens': [288206, 48, 288183, 160649, 13455751025, 10110, 5094, 288152]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3^3:C_{10}', 'transitive_degree': 60, '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: 155035121
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 91, 'group_order': 2160, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 155035168
    {'aut_label': '2A', 'centralizer': '3.a1.a1', 'counter': 2, 'group_counter': 91, 'group_order': 2160, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 6, 'size': 3}
  • id: 155035179
    {'aut_label': '2B', 'centralizer': '6.d1.a1', 'counter': 3, 'group_counter': 91, 'group_order': 2160, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 1, 'size': 6}
  • id: 155035190
    {'aut_label': '2B', 'centralizer': '6.d1.b1', 'counter': 4, 'group_counter': 91, 'group_order': 2160, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 44584, 'size': 6}
  • id: 155035201
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 5, 'group_counter': 91, 'group_order': 2160, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 721, 'size': 9}
  • id: 155035212
    {'aut_label': '2E', 'centralizer': '18.a1.a1', 'counter': 6, 'group_counter': 91, 'group_order': 2160, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 7, 'size': 18}
  • id: 155035223
    {'aut_label': '2E', 'centralizer': '18.a1.b1', 'counter': 7, 'group_counter': 91, 'group_order': 2160, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 160631, 'size': 18}
  • id: 155035234
    {'aut_label': '2G', 'centralizer': '27.a1.a1', 'counter': 8, 'group_counter': 91, 'group_order': 2160, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 727, 'size': 27}
  • id: 155035245
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 9, 'group_counter': 91, 'group_order': 2160, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 30, 'size': 2}
  • id: 155035122
    {'aut_label': '3B', 'centralizer': '4.f1.a1', 'counter': 10, 'group_counter': 91, 'group_order': 2160, 'label': '3B', 'order': 3, 'powers': [10, 1, 10], 'representative': 5760, 'size': 4}
  • id: 155035133
    {'aut_label': '3B', 'centralizer': '4.f1.b1', 'counter': 11, 'group_counter': 91, 'group_order': 2160, 'label': '3C', 'order': 3, 'powers': [11, 1, 11], 'representative': 334232, 'size': 4}
  • id: 155035144
    {'aut_label': '3D', 'centralizer': '8.d1.a1', 'counter': 12, 'group_counter': 91, 'group_order': 2160, 'label': '3D', 'order': 3, 'powers': [12, 1, 12], 'representative': 5790, 'size': 8}
  • id: 155035155
    {'aut_label': '3D', 'centralizer': '8.d1.b1', 'counter': 13, 'group_counter': 91, 'group_order': 2160, 'label': '3E', 'order': 3, 'powers': [13, 1, 13], 'representative': 334262, 'size': 8}
  • id: 155035162
    {'aut_label': '4A', 'centralizer': '18.c1.a1', 'counter': 14, 'group_counter': 91, 'group_order': 2160, 'label': '4A', 'order': 4, 'powers': [5, 14, 14], 'representative': 45304, 'size': 18}
  • id: 155035163
    {'aut_label': '4B', 'centralizer': '54.b1.a1', 'counter': 15, 'group_counter': 91, 'group_order': 2160, 'label': '4B', 'order': 4, 'powers': [5, 15, 15], 'representative': 84928, 'size': 54}
  • id: 155035164
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 91, 'group_order': 2160, 'label': '5A1', 'order': 5, 'powers': [18, 19, 1], 'representative': 25866086400, 'size': 1}
  • id: 155035165
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 91, 'group_order': 2160, 'label': '5A-1', 'order': 5, 'powers': [19, 18, 1], 'representative': 13455590400, 'size': 1}
  • id: 155035166
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 91, 'group_order': 2160, 'label': '5A2', 'order': 5, 'powers': [17, 16, 1], 'representative': 18764524800, 'size': 1}
  • id: 155035167
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 91, 'group_order': 2160, 'label': '5A-2', 'order': 5, 'powers': [16, 17, 1], 'representative': 7743859200, 'size': 1}
  • id: 155035169
    {'aut_label': '6A', 'centralizer': '12.l1.a1', 'counter': 20, 'group_counter': 91, 'group_order': 2160, 'label': '6A', 'order': 6, 'powers': [9, 3, 20], 'representative': 49, 'size': 12}
  • id: 155035170
    {'aut_label': '6B', 'centralizer': '12.e1.a1', 'counter': 21, 'group_counter': 91, 'group_order': 2160, 'label': '6B', 'order': 6, 'powers': [10, 3, 21], 'representative': 10081, 'size': 12}
  • id: 155035171
    {'aut_label': '6C', 'centralizer': '12.c1.a1', 'counter': 22, 'group_counter': 91, 'group_order': 2160, 'label': '6C', 'order': 6, 'powers': [10, 2, 22], 'representative': 10086, 'size': 12}
  • id: 155035172
    {'aut_label': '6A', 'centralizer': '12.l1.b1', 'counter': 23, 'group_counter': 91, 'group_order': 2160, 'label': '6D', 'order': 6, 'powers': [9, 4, 23], 'representative': 44632, 'size': 12}
  • id: 155035173
    {'aut_label': '6B', 'centralizer': '12.e1.b1', 'counter': 24, 'group_counter': 91, 'group_order': 2160, 'label': '6E', 'order': 6, 'powers': [11, 4, 24], 'representative': 85624, 'size': 12}
  • id: 155035174
    {'aut_label': '6C', 'centralizer': '12.c1.b1', 'counter': 25, 'group_counter': 91, 'group_order': 2160, 'label': '6F', 'order': 6, 'powers': [11, 2, 25], 'representative': 338558, 'size': 12}
  • id: 155035175
    {'aut_label': '6G', 'centralizer': '18.e1.a1', 'counter': 26, 'group_counter': 91, 'group_order': 2160, 'label': '6G', 'order': 6, 'powers': [9, 5, 26], 'representative': 751, 'size': 18}
  • id: 155035176
    {'aut_label': '6H', 'centralizer': '24.d1.a1', 'counter': 27, 'group_counter': 91, 'group_order': 2160, 'label': '6H', 'order': 6, 'powers': [12, 3, 27], 'representative': 10129, 'size': 24}
  • id: 155035177
    {'aut_label': '6H', 'centralizer': '24.d1.b1', 'counter': 28, 'group_counter': 91, 'group_order': 2160, 'label': '6I', 'order': 6, 'powers': [13, 4, 28], 'representative': 85672, 'size': 24}
  • id: 155035178
    {'aut_label': '6J', 'centralizer': '36.a1.a1', 'counter': 29, 'group_counter': 91, 'group_order': 2160, 'label': '6J', 'order': 6, 'powers': [10, 6, 29], 'representative': 10087, 'size': 36}
  • id: 155035180
    {'aut_label': '6J', 'centralizer': '36.a1.b1', 'counter': 30, 'group_counter': 91, 'group_order': 2160, 'label': '6K', 'order': 6, 'powers': [11, 7, 30], 'representative': 85630, 'size': 36}
  • id: 155035181
    {'aut_label': '10A1', 'centralizer': '3.a1.a1', 'counter': 31, 'group_counter': 91, 'group_order': 2160, 'label': '10A1', 'order': 10, 'powers': [19, 33, 2], 'representative': 13455590406, 'size': 3}
  • id: 155035182
    {'aut_label': '10A1', 'centralizer': '3.a1.a1', 'counter': 32, 'group_counter': 91, 'group_order': 2160, 'label': '10A-1', 'order': 10, 'powers': [18, 34, 2], 'representative': 25866086406, 'size': 3}
  • id: 155035183
    {'aut_label': '10A1', 'centralizer': '3.a1.a1', 'counter': 33, 'group_counter': 91, 'group_order': 2160, 'label': '10A3', 'order': 10, 'powers': [17, 32, 2], 'representative': 18764524806, 'size': 3}
  • id: 155035184
    {'aut_label': '10A1', 'centralizer': '3.a1.a1', 'counter': 34, 'group_counter': 91, 'group_order': 2160, 'label': '10A-3', 'order': 10, 'powers': [16, 31, 2], 'representative': 7743859206, 'size': 3}
  • id: 155035185
    {'aut_label': '10B1', 'centralizer': '6.d1.a1', 'counter': 35, 'group_counter': 91, 'group_order': 2160, 'label': '10B1', 'order': 10, 'powers': [19, 37, 3], 'representative': 13455590401, 'size': 6}
  • id: 155035186
    {'aut_label': '10B1', 'centralizer': '6.d1.a1', 'counter': 36, 'group_counter': 91, 'group_order': 2160, 'label': '10B-1', 'order': 10, 'powers': [18, 38, 3], 'representative': 25866086401, 'size': 6}
  • id: 155035187
    {'aut_label': '10B1', 'centralizer': '6.d1.a1', 'counter': 37, 'group_counter': 91, 'group_order': 2160, 'label': '10B3', 'order': 10, 'powers': [17, 36, 3], 'representative': 18764524801, 'size': 6}
  • id: 155035188
    {'aut_label': '10B1', 'centralizer': '6.d1.a1', 'counter': 38, 'group_counter': 91, 'group_order': 2160, 'label': '10B-3', 'order': 10, 'powers': [16, 35, 3], 'representative': 7743859201, 'size': 6}
  • id: 155035189
    {'aut_label': '10B1', 'centralizer': '6.d1.b1', 'counter': 39, 'group_counter': 91, 'group_order': 2160, 'label': '10C1', 'order': 10, 'powers': [19, 41, 4], 'representative': 13455634984, 'size': 6}
  • id: 155035191
    {'aut_label': '10B1', 'centralizer': '6.d1.b1', 'counter': 40, 'group_counter': 91, 'group_order': 2160, 'label': '10C-1', 'order': 10, 'powers': [18, 42, 4], 'representative': 25866130984, 'size': 6}
  • id: 155035192
    {'aut_label': '10B1', 'centralizer': '6.d1.b1', 'counter': 41, 'group_counter': 91, 'group_order': 2160, 'label': '10C3', 'order': 10, 'powers': [17, 40, 4], 'representative': 18764569384, 'size': 6}
  • id: 155035193
    {'aut_label': '10B1', 'centralizer': '6.d1.b1', 'counter': 42, 'group_counter': 91, 'group_order': 2160, 'label': '10C-3', 'order': 10, 'powers': [16, 39, 4], 'representative': 7743903784, 'size': 6}
  • id: 155035194
    {'aut_label': '10D1', 'centralizer': '9.a1.a1', 'counter': 43, 'group_counter': 91, 'group_order': 2160, 'label': '10D1', 'order': 10, 'powers': [16, 45, 5], 'representative': 7743859921, 'size': 9}
  • id: 155035195
    {'aut_label': '10D1', 'centralizer': '9.a1.a1', 'counter': 44, 'group_counter': 91, 'group_order': 2160, 'label': '10D-1', 'order': 10, 'powers': [17, 46, 5], 'representative': 18764525521, 'size': 9}
  • id: 155035196
    {'aut_label': '10D1', 'centralizer': '9.a1.a1', 'counter': 45, 'group_counter': 91, 'group_order': 2160, 'label': '10D3', 'order': 10, 'powers': [19, 44, 5], 'representative': 13455591121, 'size': 9}
  • id: 155035197
    {'aut_label': '10D1', 'centralizer': '9.a1.a1', 'counter': 46, 'group_counter': 91, 'group_order': 2160, 'label': '10D-3', 'order': 10, 'powers': [18, 43, 5], 'representative': 25866087121, 'size': 9}
  • id: 155035198
    {'aut_label': '10E1', 'centralizer': '18.a1.a1', 'counter': 47, 'group_counter': 91, 'group_order': 2160, 'label': '10E1', 'order': 10, 'powers': [19, 49, 6], 'representative': 13455590407, 'size': 18}
  • id: 155035199
    {'aut_label': '10E1', 'centralizer': '18.a1.a1', 'counter': 48, 'group_counter': 91, 'group_order': 2160, 'label': '10E-1', 'order': 10, 'powers': [18, 50, 6], 'representative': 25866086407, 'size': 18}
  • id: 155035200
    {'aut_label': '10E1', 'centralizer': '18.a1.a1', 'counter': 49, 'group_counter': 91, 'group_order': 2160, 'label': '10E3', 'order': 10, 'powers': [17, 48, 6], 'representative': 18764524807, 'size': 18}
  • id: 155035202
    {'aut_label': '10E1', 'centralizer': '18.a1.a1', 'counter': 50, 'group_counter': 91, 'group_order': 2160, 'label': '10E-3', 'order': 10, 'powers': [16, 47, 6], 'representative': 7743859207, 'size': 18}
  • id: 155035203
    {'aut_label': '10E1', 'centralizer': '18.a1.b1', 'counter': 51, 'group_counter': 91, 'group_order': 2160, 'label': '10F1', 'order': 10, 'powers': [19, 53, 7], 'representative': 13455751031, 'size': 18}
  • id: 155035204
    {'aut_label': '10E1', 'centralizer': '18.a1.b1', 'counter': 52, 'group_counter': 91, 'group_order': 2160, 'label': '10F-1', 'order': 10, 'powers': [18, 54, 7], 'representative': 25866247031, 'size': 18}
  • id: 155035205
    {'aut_label': '10E1', 'centralizer': '18.a1.b1', 'counter': 53, 'group_counter': 91, 'group_order': 2160, 'label': '10F3', 'order': 10, 'powers': [17, 52, 7], 'representative': 18764685431, 'size': 18}
  • id: 155035206
    {'aut_label': '10E1', 'centralizer': '18.a1.b1', 'counter': 54, 'group_counter': 91, 'group_order': 2160, 'label': '10F-3', 'order': 10, 'powers': [16, 51, 7], 'representative': 7744019831, 'size': 18}
  • id: 155035207
    {'aut_label': '10G1', 'centralizer': '27.a1.a1', 'counter': 55, 'group_counter': 91, 'group_order': 2160, 'label': '10G1', 'order': 10, 'powers': [16, 57, 8], 'representative': 7743859927, 'size': 27}
  • id: 155035208
    {'aut_label': '10G1', 'centralizer': '27.a1.a1', 'counter': 56, 'group_counter': 91, 'group_order': 2160, 'label': '10G-1', 'order': 10, 'powers': [17, 58, 8], 'representative': 18764525527, 'size': 27}
  • id: 155035209
    {'aut_label': '10G1', 'centralizer': '27.a1.a1', 'counter': 57, 'group_counter': 91, 'group_order': 2160, 'label': '10G3', 'order': 10, 'powers': [19, 56, 8], 'representative': 13455591127, 'size': 27}
  • id: 155035210
    {'aut_label': '10G1', 'centralizer': '27.a1.a1', 'counter': 58, 'group_counter': 91, 'group_order': 2160, 'label': '10G-3', 'order': 10, 'powers': [18, 55, 8], 'representative': 25866087127, 'size': 27}
  • id: 155035211
    {'aut_label': '12A', 'centralizer': '36.m1.a1', 'counter': 59, 'group_counter': 91, 'group_order': 2160, 'label': '12A', 'order': 12, 'powers': [26, 14, 59], 'representative': 44633, 'size': 36}
  • id: 155035213
    {'aut_label': '15A1', 'centralizer': '2.d1.a1', 'counter': 60, 'group_counter': 91, 'group_order': 2160, 'label': '15A1', 'order': 15, 'powers': [62, 19, 9], 'representative': 25866086448, 'size': 2}
  • id: 155035214
    {'aut_label': '15A1', 'centralizer': '2.d1.a1', 'counter': 61, 'group_counter': 91, 'group_order': 2160, 'label': '15A-1', 'order': 15, 'powers': [63, 18, 9], 'representative': 13455590430, 'size': 2}
  • id: 155035215
    {'aut_label': '15A1', 'centralizer': '2.d1.a1', 'counter': 62, 'group_counter': 91, 'group_order': 2160, 'label': '15A2', 'order': 15, 'powers': [61, 16, 9], 'representative': 18764524830, 'size': 2}
  • id: 155035216
    {'aut_label': '15A1', 'centralizer': '2.d1.a1', 'counter': 63, 'group_counter': 91, 'group_order': 2160, 'label': '15A-2', 'order': 15, 'powers': [60, 17, 9], 'representative': 7743859248, 'size': 2}
  • id: 155035217
    {'aut_label': '15B1', 'centralizer': '4.f1.a1', 'counter': 64, 'group_counter': 91, 'group_order': 2160, 'label': '15B1', 'order': 15, 'powers': [66, 19, 10], 'representative': 25866096480, 'size': 4}
  • id: 155035218
    {'aut_label': '15B1', 'centralizer': '4.f1.a1', 'counter': 65, 'group_counter': 91, 'group_order': 2160, 'label': '15B-1', 'order': 15, 'powers': [67, 18, 10], 'representative': 13455596160, 'size': 4}
  • id: 155035219
    {'aut_label': '15B1', 'centralizer': '4.f1.a1', 'counter': 66, 'group_counter': 91, 'group_order': 2160, 'label': '15B2', 'order': 15, 'powers': [65, 16, 10], 'representative': 18764530560, 'size': 4}
  • id: 155035220
    {'aut_label': '15B1', 'centralizer': '4.f1.a1', 'counter': 67, 'group_counter': 91, 'group_order': 2160, 'label': '15B-2', 'order': 15, 'powers': [64, 17, 10], 'representative': 7743869280, 'size': 4}
  • id: 155035221
    {'aut_label': '15B1', 'centralizer': '4.f1.b1', 'counter': 68, 'group_counter': 91, 'group_order': 2160, 'label': '15C1', 'order': 15, 'powers': [70, 19, 11], 'representative': 25866384633, 'size': 4}
  • id: 155035222
    {'aut_label': '15B1', 'centralizer': '4.f1.b1', 'counter': 69, 'group_counter': 91, 'group_order': 2160, 'label': '15C-1', 'order': 15, 'powers': [71, 18, 11], 'representative': 13455924632, 'size': 4}
  • id: 155035224
    {'aut_label': '15B1', 'centralizer': '4.f1.b1', 'counter': 70, 'group_counter': 91, 'group_order': 2160, 'label': '15C2', 'order': 15, 'powers': [69, 16, 11], 'representative': 18764859032, 'size': 4}
  • id: 155035225
    {'aut_label': '15B1', 'centralizer': '4.f1.b1', 'counter': 71, 'group_counter': 91, 'group_order': 2160, 'label': '15C-2', 'order': 15, 'powers': [68, 17, 11], 'representative': 7744157433, 'size': 4}
  • id: 155035226
    {'aut_label': '15D1', 'centralizer': '8.d1.a1', 'counter': 72, 'group_counter': 91, 'group_order': 2160, 'label': '15D1', 'order': 15, 'powers': [74, 19, 12], 'representative': 25866096528, 'size': 8}
  • id: 155035227
    {'aut_label': '15D1', 'centralizer': '8.d1.a1', 'counter': 73, 'group_counter': 91, 'group_order': 2160, 'label': '15D-1', 'order': 15, 'powers': [75, 18, 12], 'representative': 13455596190, 'size': 8}
  • id: 155035228
    {'aut_label': '15D1', 'centralizer': '8.d1.a1', 'counter': 74, 'group_counter': 91, 'group_order': 2160, 'label': '15D2', 'order': 15, 'powers': [73, 16, 12], 'representative': 18764530590, 'size': 8}
  • id: 155035229
    {'aut_label': '15D1', 'centralizer': '8.d1.a1', 'counter': 75, 'group_counter': 91, 'group_order': 2160, 'label': '15D-2', 'order': 15, 'powers': [72, 17, 12], 'representative': 7743869328, 'size': 8}
  • id: 155035230
    {'aut_label': '15D1', 'centralizer': '8.d1.b1', 'counter': 76, 'group_counter': 91, 'group_order': 2160, 'label': '15E1', 'order': 15, 'powers': [78, 19, 13], 'representative': 25866384681, 'size': 8}
  • id: 155035231
    {'aut_label': '15D1', 'centralizer': '8.d1.b1', 'counter': 77, 'group_counter': 91, 'group_order': 2160, 'label': '15E-1', 'order': 15, 'powers': [79, 18, 13], 'representative': 13455924662, 'size': 8}
  • id: 155035232
    {'aut_label': '15D1', 'centralizer': '8.d1.b1', 'counter': 78, 'group_counter': 91, 'group_order': 2160, 'label': '15E2', 'order': 15, 'powers': [77, 16, 13], 'representative': 18764859062, 'size': 8}
  • id: 155035233
    {'aut_label': '15D1', 'centralizer': '8.d1.b1', 'counter': 79, 'group_counter': 91, 'group_order': 2160, 'label': '15E-2', 'order': 15, 'powers': [76, 17, 13], 'representative': 7744157481, 'size': 8}
  • id: 155035235
    {'aut_label': '20A1', 'centralizer': '18.c1.a1', 'counter': 80, 'group_counter': 91, 'group_order': 2160, 'label': '20A1', 'order': 20, 'powers': [43, 82, 14], 'representative': 13455635704, 'size': 18}
  • id: 155035236
    {'aut_label': '20A1', 'centralizer': '18.c1.a1', 'counter': 81, 'group_counter': 91, 'group_order': 2160, 'label': '20A-1', 'order': 20, 'powers': [44, 83, 14], 'representative': 25866130985, 'size': 18}
  • id: 155035237
    {'aut_label': '20A1', 'centralizer': '18.c1.a1', 'counter': 82, 'group_counter': 91, 'group_order': 2160, 'label': '20A3', 'order': 20, 'powers': [45, 81, 14], 'representative': 18764569385, 'size': 18}
  • id: 155035238
    {'aut_label': '20A1', 'centralizer': '18.c1.a1', 'counter': 83, 'group_counter': 91, 'group_order': 2160, 'label': '20A-3', 'order': 20, 'powers': [46, 80, 14], 'representative': 7743904504, 'size': 18}
  • id: 155035239
    {'aut_label': '20B1', 'centralizer': '54.b1.a1', 'counter': 84, 'group_counter': 91, 'group_order': 2160, 'label': '20B1', 'order': 20, 'powers': [46, 86, 15], 'representative': 7743944128, 'size': 54}
  • id: 155035240
    {'aut_label': '20B1', 'centralizer': '54.b1.a1', 'counter': 85, 'group_counter': 91, 'group_order': 2160, 'label': '20B-1', 'order': 20, 'powers': [45, 87, 15], 'representative': 18764596048, 'size': 54}
  • id: 155035241
    {'aut_label': '20B1', 'centralizer': '54.b1.a1', 'counter': 86, 'group_counter': 91, 'group_order': 2160, 'label': '20B3', 'order': 20, 'powers': [43, 85, 15], 'representative': 13455661648, 'size': 54}
  • id: 155035242
    {'aut_label': '20B1', 'centralizer': '54.b1.a1', 'counter': 87, 'group_counter': 91, 'group_order': 2160, 'label': '20B-3', 'order': 20, 'powers': [44, 84, 15], 'representative': 25866171328, 'size': 54}
  • id: 155035243
    {'aut_label': '30A1', 'centralizer': '12.l1.a1', 'counter': 88, 'group_counter': 91, 'group_order': 2160, 'label': '30A1', 'order': 30, 'powers': [60, 35, 20], 'representative': 7743859231, 'size': 12}
  • id: 155035244
    {'aut_label': '30A1', 'centralizer': '12.l1.a1', 'counter': 89, 'group_counter': 91, 'group_order': 2160, 'label': '30A-1', 'order': 30, 'powers': [61, 36, 20], 'representative': 18764524831, 'size': 12}
  • id: 155035246
    {'aut_label': '30A1', 'centralizer': '12.l1.a1', 'counter': 90, 'group_counter': 91, 'group_order': 2160, 'label': '30A7', 'order': 30, 'powers': [62, 38, 20], 'representative': 25866086431, 'size': 12}
  • id: 155035247
    {'aut_label': '30A1', 'centralizer': '12.l1.a1', 'counter': 91, 'group_counter': 91, 'group_order': 2160, 'label': '30A-7', 'order': 30, 'powers': [63, 37, 20], 'representative': 13455590431, 'size': 12}
  • id: 155035248
    {'aut_label': '30B1', 'centralizer': '12.e1.a1', 'counter': 92, 'group_counter': 91, 'group_order': 2160, 'label': '30B1', 'order': 30, 'powers': [64, 35, 21], 'representative': 7743864961, 'size': 12}
  • id: 155035249
    {'aut_label': '30B1', 'centralizer': '12.e1.a1', 'counter': 93, 'group_counter': 91, 'group_order': 2160, 'label': '30B-1', 'order': 30, 'powers': [65, 36, 21], 'representative': 18764530561, 'size': 12}
  • id: 155035250
    {'aut_label': '30B1', 'centralizer': '12.e1.a1', 'counter': 94, 'group_counter': 91, 'group_order': 2160, 'label': '30B7', 'order': 30, 'powers': [66, 38, 21], 'representative': 25866092161, 'size': 12}
  • id: 155035251
    {'aut_label': '30B1', 'centralizer': '12.e1.a1', 'counter': 95, 'group_counter': 91, 'group_order': 2160, 'label': '30B-7', 'order': 30, 'powers': [67, 37, 21], 'representative': 13455596161, 'size': 12}
  • id: 155035252
    {'aut_label': '30C1', 'centralizer': '12.c1.a1', 'counter': 96, 'group_counter': 91, 'group_order': 2160, 'label': '30C1', 'order': 30, 'powers': [64, 31, 22], 'representative': 7743864966, 'size': 12}
  • id: 155035253
    {'aut_label': '30C1', 'centralizer': '12.c1.a1', 'counter': 97, 'group_counter': 91, 'group_order': 2160, 'label': '30C-1', 'order': 30, 'powers': [65, 32, 22], 'representative': 18764530566, 'size': 12}
  • id: 155035254
    {'aut_label': '30C1', 'centralizer': '12.c1.a1', 'counter': 98, 'group_counter': 91, 'group_order': 2160, 'label': '30C7', 'order': 30, 'powers': [66, 34, 22], 'representative': 25866092166, 'size': 12}
  • id: 155035255
    {'aut_label': '30C1', 'centralizer': '12.c1.a1', 'counter': 99, 'group_counter': 91, 'group_order': 2160, 'label': '30C-7', 'order': 30, 'powers': [67, 33, 22], 'representative': 13455596166, 'size': 12}
  • id: 155035123
    {'aut_label': '30A1', 'centralizer': '12.l1.b1', 'counter': 100, 'group_counter': 91, 'group_order': 2160, 'label': '30D1', 'order': 30, 'powers': [60, 39, 23], 'representative': 7743903814, 'size': 12}
  • id: 155035124
    {'aut_label': '30A1', 'centralizer': '12.l1.b1', 'counter': 101, 'group_counter': 91, 'group_order': 2160, 'label': '30D-1', 'order': 30, 'powers': [61, 40, 23], 'representative': 18764569414, 'size': 12}
  • id: 155035125
    {'aut_label': '30A1', 'centralizer': '12.l1.b1', 'counter': 102, 'group_counter': 91, 'group_order': 2160, 'label': '30D7', 'order': 30, 'powers': [62, 42, 23], 'representative': 25866131014, 'size': 12}
  • id: 155035126
    {'aut_label': '30A1', 'centralizer': '12.l1.b1', 'counter': 103, 'group_counter': 91, 'group_order': 2160, 'label': '30D-7', 'order': 30, 'powers': [63, 41, 23], 'representative': 13455635014, 'size': 12}
  • id: 155035127
    {'aut_label': '30B1', 'centralizer': '12.e1.b1', 'counter': 104, 'group_counter': 91, 'group_order': 2160, 'label': '30E1', 'order': 30, 'powers': [68, 39, 24], 'representative': 7743930425, 'size': 12}
  • id: 155035128
    {'aut_label': '30B1', 'centralizer': '12.e1.b1', 'counter': 105, 'group_counter': 91, 'group_order': 2160, 'label': '30E-1', 'order': 30, 'powers': [69, 40, 24], 'representative': 18764596025, 'size': 12}
  • id: 155035129
    {'aut_label': '30B1', 'centralizer': '12.e1.b1', 'counter': 106, 'group_counter': 91, 'group_order': 2160, 'label': '30E7', 'order': 30, 'powers': [70, 42, 24], 'representative': 25866157625, 'size': 12}
  • id: 155035130
    {'aut_label': '30B1', 'centralizer': '12.e1.b1', 'counter': 107, 'group_counter': 91, 'group_order': 2160, 'label': '30E-7', 'order': 30, 'powers': [71, 41, 24], 'representative': 13455661625, 'size': 12}
  • id: 155035131
    {'aut_label': '30C1', 'centralizer': '12.c1.b1', 'counter': 108, 'group_counter': 91, 'group_order': 2160, 'label': '30F1', 'order': 30, 'powers': [68, 31, 25], 'representative': 7744153119, 'size': 12}
  • id: 155035132
    {'aut_label': '30C1', 'centralizer': '12.c1.b1', 'counter': 109, 'group_counter': 91, 'group_order': 2160, 'label': '30F-1', 'order': 30, 'powers': [69, 32, 25], 'representative': 18764818719, 'size': 12}
  • id: 155035134
    {'aut_label': '30C1', 'centralizer': '12.c1.b1', 'counter': 110, 'group_counter': 91, 'group_order': 2160, 'label': '30F7', 'order': 30, 'powers': [70, 34, 25], 'representative': 25866380319, 'size': 12}
  • id: 155035135
    {'aut_label': '30C1', 'centralizer': '12.c1.b1', 'counter': 111, 'group_counter': 91, 'group_order': 2160, 'label': '30F-7', 'order': 30, 'powers': [71, 33, 25], 'representative': 13455884319, 'size': 12}
  • id: 155035136
    {'aut_label': '30G1', 'centralizer': '18.e1.a1', 'counter': 112, 'group_counter': 91, 'group_order': 2160, 'label': '30G1', 'order': 30, 'powers': [62, 43, 26], 'representative': 25866087169, 'size': 18}
  • id: 155035137
    {'aut_label': '30G1', 'centralizer': '18.e1.a1', 'counter': 113, 'group_counter': 91, 'group_order': 2160, 'label': '30G-1', 'order': 30, 'powers': [63, 44, 26], 'representative': 13455591151, 'size': 18}
  • id: 155035138
    {'aut_label': '30G1', 'centralizer': '18.e1.a1', 'counter': 114, 'group_counter': 91, 'group_order': 2160, 'label': '30G7', 'order': 30, 'powers': [61, 46, 26], 'representative': 18764525569, 'size': 18}
  • id: 155035139
    {'aut_label': '30G1', 'centralizer': '18.e1.a1', 'counter': 115, 'group_counter': 91, 'group_order': 2160, 'label': '30G-7', 'order': 30, 'powers': [60, 45, 26], 'representative': 7743859951, 'size': 18}
  • id: 155035140
    {'aut_label': '30H1', 'centralizer': '24.d1.a1', 'counter': 116, 'group_counter': 91, 'group_order': 2160, 'label': '30H1', 'order': 30, 'powers': [72, 35, 27], 'representative': 7743864991, 'size': 24}
  • id: 155035141
    {'aut_label': '30H1', 'centralizer': '24.d1.a1', 'counter': 117, 'group_counter': 91, 'group_order': 2160, 'label': '30H-1', 'order': 30, 'powers': [73, 36, 27], 'representative': 18764530591, 'size': 24}
  • id: 155035142
    {'aut_label': '30H1', 'centralizer': '24.d1.a1', 'counter': 118, 'group_counter': 91, 'group_order': 2160, 'label': '30H7', 'order': 30, 'powers': [74, 38, 27], 'representative': 25866092191, 'size': 24}
  • id: 155035143
    {'aut_label': '30H1', 'centralizer': '24.d1.a1', 'counter': 119, 'group_counter': 91, 'group_order': 2160, 'label': '30H-7', 'order': 30, 'powers': [75, 37, 27], 'representative': 13455596191, 'size': 24}
  • id: 155035145
    {'aut_label': '30H1', 'centralizer': '24.d1.b1', 'counter': 120, 'group_counter': 91, 'group_order': 2160, 'label': '30I1', 'order': 30, 'powers': [76, 39, 28], 'representative': 7743930455, 'size': 24}
  • id: 155035146
    {'aut_label': '30H1', 'centralizer': '24.d1.b1', 'counter': 121, 'group_counter': 91, 'group_order': 2160, 'label': '30I-1', 'order': 30, 'powers': [77, 40, 28], 'representative': 18764596055, 'size': 24}
  • id: 155035147
    {'aut_label': '30H1', 'centralizer': '24.d1.b1', 'counter': 122, 'group_counter': 91, 'group_order': 2160, 'label': '30I7', 'order': 30, 'powers': [78, 42, 28], 'representative': 25866157655, 'size': 24}
  • id: 155035148
    {'aut_label': '30H1', 'centralizer': '24.d1.b1', 'counter': 123, 'group_counter': 91, 'group_order': 2160, 'label': '30I-7', 'order': 30, 'powers': [79, 41, 28], 'representative': 13455661655, 'size': 24}
  • id: 155035149
    {'aut_label': '30J1', 'centralizer': '36.a1.a1', 'counter': 124, 'group_counter': 91, 'group_order': 2160, 'label': '30J1', 'order': 30, 'powers': [64, 47, 29], 'representative': 7743864967, 'size': 36}
  • id: 155035150
    {'aut_label': '30J1', 'centralizer': '36.a1.a1', 'counter': 125, 'group_counter': 91, 'group_order': 2160, 'label': '30J-1', 'order': 30, 'powers': [65, 48, 29], 'representative': 18764530567, 'size': 36}
  • id: 155035151
    {'aut_label': '30J1', 'centralizer': '36.a1.a1', 'counter': 126, 'group_counter': 91, 'group_order': 2160, 'label': '30J7', 'order': 30, 'powers': [66, 50, 29], 'representative': 25866092167, 'size': 36}
  • id: 155035152
    {'aut_label': '30J1', 'centralizer': '36.a1.a1', 'counter': 127, 'group_counter': 91, 'group_order': 2160, 'label': '30J-7', 'order': 30, 'powers': [67, 49, 29], 'representative': 13455596167, 'size': 36}
  • id: 155035153
    {'aut_label': '30J1', 'centralizer': '36.a1.b1', 'counter': 128, 'group_counter': 91, 'group_order': 2160, 'label': '30K1', 'order': 30, 'powers': [68, 51, 30], 'representative': 7743930431, 'size': 36}
  • id: 155035154
    {'aut_label': '30J1', 'centralizer': '36.a1.b1', 'counter': 129, 'group_counter': 91, 'group_order': 2160, 'label': '30K-1', 'order': 30, 'powers': [69, 52, 30], 'representative': 18764596031, 'size': 36}
  • id: 155035156
    {'aut_label': '30J1', 'centralizer': '36.a1.b1', 'counter': 130, 'group_counter': 91, 'group_order': 2160, 'label': '30K7', 'order': 30, 'powers': [70, 54, 30], 'representative': 25866157631, 'size': 36}
  • id: 155035157
    {'aut_label': '30J1', 'centralizer': '36.a1.b1', 'counter': 131, 'group_counter': 91, 'group_order': 2160, 'label': '30K-7', 'order': 30, 'powers': [71, 53, 30], 'representative': 13455661631, 'size': 36}
  • id: 155035158
    {'aut_label': '60A1', 'centralizer': '36.m1.a1', 'counter': 132, 'group_counter': 91, 'group_order': 2160, 'label': '60A1', 'order': 60, 'powers': [112, 80, 59], 'representative': 7743903815, 'size': 36}
  • id: 155035159
    {'aut_label': '60A1', 'centralizer': '36.m1.a1', 'counter': 133, 'group_counter': 91, 'group_order': 2160, 'label': '60A-1', 'order': 60, 'powers': [113, 81, 59], 'representative': 18764569415, 'size': 36}
  • id: 155035160
    {'aut_label': '60A1', 'centralizer': '36.m1.a1', 'counter': 134, 'group_counter': 91, 'group_order': 2160, 'label': '60A7', 'order': 60, 'powers': [114, 83, 59], 'representative': 25866131015, 'size': 36}
  • id: 155035161
    {'aut_label': '60A1', 'centralizer': '36.m1.a1', 'counter': 135, 'group_counter': 91, 'group_order': 2160, 'label': '60A-7', 'order': 60, 'powers': [115, 82, 59], 'representative': 13455635015, 'size': 36}
• 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: 15048721
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.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], 'schur_index': 1}
  • id: 15048732
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.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], 'schur_index': 1}
  • id: 15048743
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 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: 15048754
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 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: 15048765
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 15048771
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 15048772
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 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: 15048773
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 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: 15048729
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 0, 0, 0, -1, 2, 2, -1, -1, 2, 0, 2, 2, 2, 2, -1, 0, 2, 0, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15048730
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, -2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 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, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048731
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, 0, -2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 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, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048733
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, -2, 2, 0, 0, 0, -1, 2, 2, -1, -1, 2, 0, 2, 2, 2, 2, 1, 0, -2, 0, -2, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15048734
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 2, 2, 0, 0, 0, -1, 2, 2, -1, -1, -2, 0, 2, 2, 2, 2, 1, 0, 2, 0, -2, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15048735
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, -2, 2, 0, 0, 0, -1, 2, 2, -1, -1, -2, 0, 2, 2, 2, 2, -1, 0, -2, 0, 2, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15048774
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1i', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 15048722
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1j', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 4, -4, 4, 4, 4, 4, 4, 4, -4, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 15048723
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1k', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, -4, 4, -1, -1, -1, -1, -4, -4, 4, -4, -4, 4, 4, -4, 4, 4, -4, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -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: 15048724
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1l', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, -4, 4, -1, -1, -1, -1, 4, -4, -4, -4, 4, -4, 4, 4, -4, -4, 4, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -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: 15048725
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1m', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 4, -4, -1, -1, -1, -1, 4, -4, 4, -4, 4, 4, 4, 4, 4, -4, -4, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 15048726
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1n', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -4, 4, -4, 4, -4, -4, 4, -4, -4, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 15048727
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1o', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 4, -4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -4, 4, 4, 4, -4, 4, 4, -4, 4, -4, 4, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -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: 15048728
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.1p', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 4, 4, -4, 4, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, 4, 4, -4, 4, 4, -4, 4, 4, -4, 4, -4, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -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: 15048742
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 2, 0, 0, 2, 0, 4, -2, 1, -2, 1, 0, 0, 4, 4, 4, 4, 0, 1, -1, -2, 0, 2, 0, 0, -1, 0, -1, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048744
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 2, 0, 0, 2, 0, 0, 4, 1, -2, 1, -2, 0, 0, 4, 4, 4, 4, 2, -2, 0, 1, -1, 0, 0, -1, 0, -1, 0, 4, 4, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048745
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 0, 0, 0, -4, 0, 0, 0, -2, 4, 4, -2, -2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, 4, 4, 4, 4, 4, 4, 4, -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, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048746
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, -2, 0, 0, -2, 0, 0, 4, 1, -2, 1, -2, 0, 0, 4, 4, 4, 4, -2, -2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048747
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4e', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 0, -2, 0, 0, -2, 0, 4, -2, 1, -2, 1, 0, 0, 4, 4, 4, 4, 0, 1, 1, -2, 0, -2, 0, 0, 1, 0, 1, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048748
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4f', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, -2, 0, 0, 2, 0, 0, 4, 1, -2, 1, -2, 0, 0, 4, 4, 4, 4, -2, 2, 0, -1, 1, 0, 0, 1, 0, -1, 0, -4, -4, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048749
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4g', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 0, -2, 0, 0, 2, 0, 4, -2, 1, -2, 1, 0, 0, 4, 4, 4, 4, 0, -1, 1, 2, 0, -2, 0, 0, 1, 0, -1, -4, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048750
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4h', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 0, 2, 0, 0, -2, 0, 4, -2, 1, -2, 1, 0, 0, 4, 4, 4, 4, 0, -1, -1, 2, 0, 2, 0, 0, -1, 0, 1, -4, -4, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048751
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4i', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 2, 0, 0, -2, 0, 0, 4, 1, -2, 1, -2, 0, 0, 4, 4, 4, 4, 2, 2, 0, -1, -1, 0, 0, -1, 0, 1, 0, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048736
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2g', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 0, 0, 0, -4, 8, 8, -4, -4, 8, 0, -2, -2, -2, -2, -4, 0, 8, 0, 8, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15048737
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2h', 'multiplicity': 4, 'nt': [20, 12], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, -2, -2, -2, -2, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, -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, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048738
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2i', 'multiplicity': 4, 'nt': [20, 12], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -8, 0, 0, -8, 8, 8, 8, 8, 8, 0, 0, -2, -2, -2, -2, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, -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, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048739
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2j', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 0, -8, -8, 8, 0, 0, 0, -4, 8, 8, -4, -4, 8, 0, -2, -2, -2, -2, 4, 0, -8, 0, -8, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15048740
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2k', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 0, -8, 8, 8, 0, 0, 0, -4, 8, 8, -4, -4, -8, 0, -2, -2, -2, -2, 4, 0, 8, 0, -8, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15048741
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.2l', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 0, 8, -8, 8, 0, 0, 0, -4, 8, 8, -4, -4, -8, 0, -2, -2, -2, -2, -4, 0, -8, 0, 8, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15048762
    {'cdim': 8, 'counter': 47, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8a', 'multiplicity': 1, 'nt': [12, 156], 'qdim': 8, 'qvalues': [8, 0, 0, 4, 0, 0, 0, 0, -4, -4, 2, 2, -1, 0, 0, 8, 8, 8, 8, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048763
    {'cdim': 8, 'counter': 48, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8b', 'multiplicity': 1, 'nt': [12, 156], 'qdim': 8, 'qvalues': [8, 0, 4, 0, 0, 0, 0, 0, -4, 2, -4, -1, 2, 0, 0, 8, 8, 8, 8, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048764
    {'cdim': 8, 'counter': 49, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8c', 'multiplicity': 1, 'nt': [24, 1322], 'qdim': 8, 'qvalues': [8, 0, -4, 0, 0, 0, 0, 0, -4, 2, -4, -1, 2, 0, 0, 8, 8, 8, 8, 2, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048766
    {'cdim': 8, 'counter': 50, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8d', 'multiplicity': 1, 'nt': [24, 1322], 'qdim': 8, 'qvalues': [8, 0, 0, -4, 0, 0, 0, 0, -4, -4, 2, 2, -1, 0, 0, 8, 8, 8, 8, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048752
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4j', 'multiplicity': 4, 'nt': [30, 82], 'qdim': 16, 'qvalues': [16, 16, 0, 8, 0, 0, 8, 0, 16, -8, 4, -8, 4, 0, 0, -4, -4, -4, -4, 0, 4, -4, -8, 0, 8, 0, 0, -4, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048753
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4k', 'multiplicity': 4, 'nt': [30, 82], 'qdim': 16, 'qvalues': [16, 16, 8, 0, 0, 8, 0, 0, 16, 4, -8, 4, -8, 0, 0, -4, -4, -4, -4, 8, -8, 0, 4, -4, 0, 0, -4, 0, -4, 0, -4, -4, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048755
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4l', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, -8, 0, 0, 8, 0, 0, 16, 4, -8, 4, -8, 0, 0, -4, -4, -4, -4, -8, 8, 0, -4, 4, 0, 0, 4, 0, -4, 0, 4, 4, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048756
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4m', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 0, -8, 0, 0, 8, 0, 16, -8, 4, -8, 4, 0, 0, -4, -4, -4, -4, 0, -4, 4, 8, 0, -8, 0, 0, 4, 0, -4, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048757
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4n', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 8, 0, 0, -8, 0, 16, -8, 4, -8, 4, 0, 0, -4, -4, -4, -4, 0, -4, -4, 8, 0, 8, 0, 0, -4, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048758
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4o', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 8, 0, 0, -8, 0, 0, 16, 4, -8, 4, -8, 0, 0, -4, -4, -4, -4, 8, 8, 0, -4, -4, 0, 0, -4, 0, 4, 0, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048759
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4p', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -16, 0, 0, 0, -8, 16, 16, -8, -8, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, 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, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048760
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4q', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, -8, 0, 0, -8, 0, 0, 16, 4, -8, 4, -8, 0, 0, -4, -4, -4, -4, -8, -8, 0, 4, 4, 0, 0, 4, 0, 4, 0, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048761
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.4r', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, 0, -8, 0, 0, -8, 0, 16, -8, 4, -8, 4, 0, 0, -4, -4, -4, -4, 0, 4, 4, -8, 0, -8, 0, 0, 4, 0, 4, -4, -4, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048767
    {'cdim': 8, 'counter': 51, 'faithful': True, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8e', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 16, 0, 0, 0, 0, -16, -16, 8, 8, -4, 0, 0, -8, -8, -8, -8, 0, 0, -8, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048768
    {'cdim': 8, 'counter': 52, 'faithful': True, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8f', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 32, 'qvalues': [32, 0, 16, 0, 0, 0, 0, 0, -16, 8, -16, -4, 8, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048769
    {'cdim': 8, 'counter': 53, 'faithful': True, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8g', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 32, 'qvalues': [32, 0, -16, 0, 0, 0, 0, 0, -16, 8, -16, -4, 8, 0, 0, -8, -8, -8, -8, 8, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, 4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15048770
    {'cdim': 8, 'counter': 54, 'faithful': True, 'group': '2160.dm', 'group_order': 2160, 'image': None, 'label': '2160.dm.8h', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -16, 0, 0, 0, 0, -16, -16, 8, 8, -4, 0, 0, -8, -8, -8, -8, 0, 0, 8, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 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: 34770160
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 2160, 'label': '2160.dm.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]]]}
  • id: 34770207
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 1080, 'label': '2160.dm.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 34770218
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 1080, 'label': '2160.dm.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 34770229
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 1080, 'label': '2160.dm.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 34770240
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 1080, 'label': '2160.dm.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 34770251
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 1080, 'label': '2160.dm.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 34770262
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 1080, 'label': '2160.dm.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 34770273
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1080, 'label': '2160.dm.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 34770284
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 432, 'label': '2160.dm.1i1', 'nt': [5, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770161
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 432, 'label': '2160.dm.1i2', 'nt': [5, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770172
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 432, 'label': '2160.dm.1i3', 'nt': [5, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770183
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 432, 'label': '2160.dm.1i4', 'nt': [5, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770194
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.e1.a1', 'kernel_order': 216, 'label': '2160.dm.1j1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770201
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.e1.a1', 'kernel_order': 216, 'label': '2160.dm.1j2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770202
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.e1.a1', 'kernel_order': 216, 'label': '2160.dm.1j3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770203
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.e1.a1', 'kernel_order': 216, 'label': '2160.dm.1j4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770204
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.b1', 'kernel_order': 216, 'label': '2160.dm.1k1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770205
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.b1', 'kernel_order': 216, 'label': '2160.dm.1k2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770206
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.b1', 'kernel_order': 216, 'label': '2160.dm.1k3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770208
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.b1', 'kernel_order': 216, 'label': '2160.dm.1k4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770209
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 21, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 216, 'label': '2160.dm.1l1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770210
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 22, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 216, 'label': '2160.dm.1l2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770211
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 23, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 216, 'label': '2160.dm.1l3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770212
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 24, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 216, 'label': '2160.dm.1l4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770213
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 25, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 216, 'label': '2160.dm.1m1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770214
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 26, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 216, 'label': '2160.dm.1m2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770215
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 27, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 216, 'label': '2160.dm.1m3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770216
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 28, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 216, 'label': '2160.dm.1m4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770217
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 29, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 216, 'label': '2160.dm.1n1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770219
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 30, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 216, 'label': '2160.dm.1n2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770220
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 31, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 216, 'label': '2160.dm.1n3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770221
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 32, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 216, 'label': '2160.dm.1n4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770222
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 33, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.b1', 'kernel_order': 216, 'label': '2160.dm.1o1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770223
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 34, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.b1', 'kernel_order': 216, 'label': '2160.dm.1o2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770224
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 35, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.b1', 'kernel_order': 216, 'label': '2160.dm.1o3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770225
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 36, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.b1', 'kernel_order': 216, 'label': '2160.dm.1o4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770226
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 37, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 216, 'label': '2160.dm.1p1', 'nt': [10, 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, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770227
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 38, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 216, 'label': '2160.dm.1p2', 'nt': [10, 4], '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, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770228
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 39, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 216, 'label': '2160.dm.1p3', 'nt': [10, 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, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770230
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2160, 'counter': 40, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 216, 'label': '2160.dm.1p4', 'nt': [10, 4], '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, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770231
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 41, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 360, 'label': '2160.dm.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[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]], [[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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34770232
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 42, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 270, 'label': '2160.dm.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770233
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 43, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 270, 'label': '2160.dm.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770234
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 44, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 180, 'label': '2160.dm.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 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]], [[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]], [[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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34770235
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 45, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 180, 'label': '2160.dm.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 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]], [[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]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34770236
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 46, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 180, 'label': '2160.dm.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 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]], [[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]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34770237
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 47, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 72, 'label': '2160.dm.2g1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[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]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770238
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 48, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 72, 'label': '2160.dm.2g2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[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]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770239
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 49, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 72, 'label': '2160.dm.2g3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -1]], [[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]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770241
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 50, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 72, 'label': '2160.dm.2g4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 1]], [[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]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770242
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 51, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.c1.a1', 'kernel_order': 54, 'label': '2160.dm.2h1', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[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]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[-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]]]}
  • id: 34770243
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 52, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.c1.a1', 'kernel_order': 54, 'label': '2160.dm.2h2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[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]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[-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]]]}
  • id: 34770244
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 53, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.c1.a1', 'kernel_order': 54, 'label': '2160.dm.2h3', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[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]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-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]]]}
  • id: 34770245
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 54, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.c1.a1', 'kernel_order': 54, 'label': '2160.dm.2h4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[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]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-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]]]}
  • id: 34770246
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 55, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 54, 'label': '2160.dm.2i1', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[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]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[-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]]]}
  • id: 34770247
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 56, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 54, 'label': '2160.dm.2i2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[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]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[-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]]]}
  • id: 34770248
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 57, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 54, 'label': '2160.dm.2i3', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[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]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-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]]]}
  • id: 34770249
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 540, 'counter': 58, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 54, 'label': '2160.dm.2i4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[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]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-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]]]}
  • id: 34770250
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 59, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 36, 'label': '2160.dm.2j1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[2, 2]], [[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]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]]]}
  • id: 34770252
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 60, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 36, 'label': '2160.dm.2j2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[2, -2]], [[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]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]]]}
  • id: 34770253
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 61, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 36, 'label': '2160.dm.2j3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[2, 1]], [[2, 2]], [[2, -1]], [[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]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]]]}
  • id: 34770254
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 62, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 36, 'label': '2160.dm.2j4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[2, -1]], [[2, -2]], [[2, 1]], [[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]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]]]}
  • id: 34770255
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 63, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 36, 'label': '2160.dm.2k1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[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]], [[1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770256
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 64, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 36, 'label': '2160.dm.2k2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[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]], [[1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770257
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 65, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 36, 'label': '2160.dm.2k3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -1]], [[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]], [[1, 0]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770258
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 66, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 36, 'label': '2160.dm.2k4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 1]], [[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]], [[1, 0]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770259
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 67, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 36, 'label': '2160.dm.2l1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[2, 2]], [[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]], [[1, 0]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]]]}
  • id: 34770260
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 68, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 36, 'label': '2160.dm.2l2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[2, -2]], [[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]], [[1, 0]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]]]}
  • id: 34770261
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 69, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 36, 'label': '2160.dm.2l3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[2, 1]], [[2, 2]], [[2, -1]], [[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]], [[1, 0]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]]]}
  • id: 34770263
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 360, 'counter': 70, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 36, 'label': '2160.dm.2l4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[2, -1]], [[2, -2]], [[2, 1]], [[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]], [[1, 0]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]]]}
  • id: 34770264
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 71, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 30, 'label': '2160.dm.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770265
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 72, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 30, 'label': '2160.dm.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 34770266
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 90, 'counter': 73, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 45, 'label': '2160.dm.4c', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34770267
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 74, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 30, 'label': '2160.dm.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 34770268
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 75, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 30, 'label': '2160.dm.4e', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770269
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 76, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 15, 'label': '2160.dm.4f', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 34770270
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 77, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 15, 'label': '2160.dm.4g', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770271
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 78, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 15, 'label': '2160.dm.4h', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770272
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 79, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 15, 'label': '2160.dm.4i', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 34770274
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 80, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4j1', 'nt': [30, 82], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, 1]], [[4, 2]], [[4, -1]], [[4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770275
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 81, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4j2', 'nt': [30, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, -1]], [[4, -2]], [[4, 1]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770276
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 82, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4j3', 'nt': [30, 82], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, -2]], [[4, 1]], [[4, 2]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[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]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770277
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 83, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4j4', 'nt': [30, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, 2]], [[4, -1]], [[4, -2]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[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]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770278
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 84, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4k1', 'nt': [30, 82], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -1]], [[4, -2]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770279
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 85, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4k2', 'nt': [30, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 1]], [[4, 2]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770280
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 86, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4k3', 'nt': [30, 82], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, 2]], [[4, -1]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770281
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 87, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4k4', 'nt': [30, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, -2]], [[4, 1]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770282
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 88, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4l1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770283
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 89, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4l2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770285
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 90, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4l3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770286
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 91, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4l4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770287
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 92, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4m1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770288
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 93, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4m2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770289
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 94, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4m3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[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]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770290
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 95, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4m4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[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]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770291
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 96, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4n1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770292
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 97, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4n2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770293
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 98, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4n3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[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]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770294
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 99, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4n4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[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]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770162
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 100, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4o1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770163
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 101, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4o2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770164
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 102, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4o3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770165
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 103, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '720.808', 'image_order': 720, 'indicator': 0, 'kernel': '720.a1.a1', 'kernel_order': 3, 'label': '2160.dm.4o4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770166
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 90, 'counter': 104, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '240.169', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 9, 'label': '2160.dm.4p1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, -2]], [[4, 2]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-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]], [[2, -1]], [[2, 2]], [[2, 1]], [[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]]]}
  • id: 34770167
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 90, 'counter': 105, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '240.169', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 9, 'label': '2160.dm.4p2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[4, 1]], [[4, -1]], [[4, 2]], [[4, -2]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-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]], [[2, 1]], [[2, -2]], [[2, -1]], [[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]]]}
  • id: 34770168
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 90, 'counter': 106, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '240.169', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 9, 'label': '2160.dm.4p3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-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]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[4, 2]], [[4, -2]], [[4, -1]], [[4, 1]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-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]], [[2, 2]], [[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]]]}
  • id: 34770169
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 90, 'counter': 107, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '240.169', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 9, 'label': '2160.dm.4p4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-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]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[4, -2]], [[4, 2]], [[4, 1]], [[4, -1]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-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]], [[2, -2]], [[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]]]}
  • id: 34770170
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 108, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4q1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -1]], [[4, -2]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770171
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 109, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4q2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 1]], [[4, 2]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770173
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 110, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4q3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, 2]], [[4, -1]], [[-2, -1]], [[-2, -2]], [[-2, 1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770174
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 111, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4q4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, -2]], [[4, 1]], [[-2, 1]], [[-2, 2]], [[-2, -1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770175
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 112, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4r1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[4, 2]], [[4, -1]], [[4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -2]], [[4, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770176
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 113, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4r2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, -1]], [[4, -2]], [[4, 1]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 2]], [[4, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770177
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 114, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4r3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 2]], [[4, -2]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, -2]], [[4, 1]], [[4, 2]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, -1]], [[4, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[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]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770178
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 30, 'counter': 115, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '360.132', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 6, 'label': '2160.dm.4r4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -2]], [[4, 2]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, 2]], [[4, -1]], [[4, -2]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, 1]], [[4, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[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]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770179
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 116, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '432.741', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 5, 'label': '2160.dm.8a', 'nt': [12, 156], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770180
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 117, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '432.741', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 5, 'label': '2160.dm.8b', 'nt': [12, 156], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34770181
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 118, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '432.741', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 5, 'label': '2160.dm.8c', 'nt': [24, 1322], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 34770182
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 119, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '432.741', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 5, 'label': '2160.dm.8d', 'nt': [24, 1322], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34770184
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 120, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8e1', 'nt': [60, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, -2]], [[8, 2]], [[8, -1]], [[8, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-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]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[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]]]}
  • id: 34770185
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 121, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8e2', 'nt': [60, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 2]], [[8, -2]], [[8, 1]], [[8, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-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]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[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]]]}
  • id: 34770186
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 122, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8e3', 'nt': [60, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[8, 2]], [[8, -2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -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]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-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]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[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]]]}
  • id: 34770187
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 123, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8e4', 'nt': [60, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[8, -2]], [[8, 2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 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]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-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]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[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]]]}
  • id: 34770188
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 124, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8f1', 'nt': [60, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, -2]], [[8, 2]], [[8, -1]], [[8, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 1]], [[4, 2]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[-4, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-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]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[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]]]}
  • id: 34770189
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 125, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8f2', 'nt': [60, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 2]], [[8, -2]], [[8, 1]], [[8, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -1]], [[4, -2]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[-4, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-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]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[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]]]}
  • id: 34770190
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 126, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8f3', 'nt': [60, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[8, 2]], [[8, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, -2]], [[4, 1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[-4, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-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]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[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]]]}
  • id: 34770191
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 127, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8f4', 'nt': [60, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[8, -2]], [[8, 2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 2]], [[4, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[-4, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-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]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[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]]]}
  • id: 34770192
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 128, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8g1', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, -2]], [[8, 2]], [[8, -1]], [[8, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[-4, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[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]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-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]]]}
  • id: 34770193
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 129, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8g2', 'nt': [120, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 2]], [[8, -2]], [[8, 1]], [[8, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[-4, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[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]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-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]]]}
  • id: 34770195
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 130, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8g3', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[8, 2]], [[8, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[-4, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[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]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-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]]]}
  • id: 34770196
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 131, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8g4', 'nt': [120, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[8, -2]], [[8, 2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[-4, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[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]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-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]]]}
  • id: 34770197
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 132, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8h1', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, -2]], [[8, 2]], [[8, -1]], [[8, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[-4, 1]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-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]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-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]]]}
  • id: 34770198
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 133, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8h2', 'nt': [120, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 2]], [[8, -2]], [[8, 1]], [[8, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[-4, -1]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-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]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-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]]]}
  • id: 34770199
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 134, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8h3', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[8, 2]], [[8, -2]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[-4, -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]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[-4, -2]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-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]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-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]]]}
  • id: 34770200
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 5, 'counter': 135, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '2160.dm', 'group_counter': 91, 'group_order': 2160, 'image': None, 'image_isoclass': '2160.dm', 'image_order': 2160, 'indicator': 0, 'kernel': '2160.a1.a1', 'kernel_order': 1, 'label': '2160.dm.8h4', 'nt': [120, 4], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[8, -2]], [[8, 2]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[-4, 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]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[-4, 2]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-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]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-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]]]}
• 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: 168862467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 2160, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '2160.dm.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': '2160.dm', 'subgroup_hash': 5240928682237879649, 'subgroup_order': 2160, 'subgroup_tex': 'S_3^3:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 168862578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1080, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.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': '1080.538', 'subgroup_hash': 538, 'subgroup_order': 1080, 'subgroup_tex': 'C_5\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1080, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.538', 'subgroup_hash': 538, 'subgroup_order': 1080, 'subgroup_tex': 'C_5\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 1080, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.514', 'subgroup_hash': 514, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times C_3^2:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 168862796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1080, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.523', 'subgroup_hash': 523, 'subgroup_order': 1080, 'subgroup_tex': 'C_5\\times S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 168862807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1080, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.523', 'subgroup_hash': 523, 'subgroup_order': 1080, 'subgroup_tex': 'C_5\\times S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 168862818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 1080, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.520', 'subgroup_hash': 520, 'subgroup_order': 1080, 'subgroup_tex': 'S_3^2:C_{30}', 'supersolvable': False, 'sylow': 0}
  • id: 168862829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 1080, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1080.527', 'subgroup_hash': 527, 'subgroup_order': 1080, 'subgroup_tex': 'C_5\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 168862840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 360, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.808', 'subgroup_hash': 808, 'subgroup_order': 720, 'subgroup_tex': 'C_{10}\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 168862468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 540, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '540.105', 'subgroup_hash': 105, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 540, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.101', 'subgroup_hash': 101, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 540, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.101', 'subgroup_hash': 101, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 540, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.109', 'subgroup_hash': 109, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 540, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.109', 'subgroup_hash': 109, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 540, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.93', 'subgroup_hash': 93, 'subgroup_order': 540, 'subgroup_tex': 'C_3^2:C_{60}', 'supersolvable': False, 'sylow': 0}
  • id: 168862534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 540, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.96', 'subgroup_hash': 96, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 168862545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 270, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '540.101', 'subgroup_hash': 101, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 270, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '540.101', 'subgroup_hash': 101, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 270, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '540.105', 'subgroup_hash': 105, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 270, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '540.105', 'subgroup_hash': 105, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': True, 'core_order': 432, 'counter': 21, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '2160.dm.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 168862601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 30, 'characteristic': True, 'core_order': 360, 'counter': 22, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2160.dm.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.132', 'subgroup_hash': 132, 'subgroup_order': 360, 'subgroup_tex': 'S_3^2:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 168862612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '360.153', 'subgroup_hash': 153, 'subgroup_order': 360, 'subgroup_tex': 'C_{10}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '360.153', 'subgroup_hash': 153, 'subgroup_order': 360, 'subgroup_tex': 'C_{10}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.148', 'subgroup_hash': 148, 'subgroup_order': 360, 'subgroup_tex': 'C_2\\times C_3^2:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 168862645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.153', 'subgroup_hash': 153, 'subgroup_order': 360, 'subgroup_tex': 'C_{10}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.153', 'subgroup_hash': 153, 'subgroup_order': 360, 'subgroup_tex': 'C_{10}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.132', 'subgroup_hash': 132, 'subgroup_order': 360, 'subgroup_tex': 'S_3^2:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 168862678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.132', 'subgroup_hash': 132, 'subgroup_order': 360, 'subgroup_tex': 'S_3^2:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 168862690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 180, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '360.132', 'subgroup_hash': 132, 'subgroup_order': 360, 'subgroup_tex': 'S_3^2:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 168862701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': True, 'core_order': 270, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '270.24', 'subgroup_hash': 24, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 270, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 270, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '270.28', 'subgroup_hash': 28, 'subgroup_order': 270, 'subgroup_tex': 'C_3^3:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 135, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.24', 'subgroup_hash': 24, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 135, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '270.24', 'subgroup_hash': 24, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 135, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 135, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.169', 'subgroup_hash': 169, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 216, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 216, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 216, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 168862788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 216, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 168862789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 216, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 168862790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 216, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 168862791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 216, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 168862792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 180, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 180, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 180, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.23', 'subgroup_hash': 23, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 168862795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 45, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 45, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 90, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.35', 'subgroup_hash': 35, 'subgroup_order': 180, 'subgroup_tex': 'C_{30}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.35', 'subgroup_hash': 35, 'subgroup_order': 180, 'subgroup_tex': 'C_{30}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.35', 'subgroup_hash': 35, 'subgroup_order': 180, 'subgroup_tex': 'C_{30}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 45, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 45, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '180.33', 'subgroup_hash': 33, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 90, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 90, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 90, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.23', 'subgroup_hash': 23, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 168862822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 72, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 168862823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': True, 'core_order': 135, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '2160.dm.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 168862830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '120.23', 'subgroup_hash': 23, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 168862834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 108, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 108, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 108, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 108, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 108, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 108, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 168862841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 108, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 168862842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 54, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 54, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.20.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 54, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 54, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.20.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 90, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 30, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 30, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 15, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 15, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862470
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 15, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862471
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 15, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 5, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 5, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862474
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862475
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862477
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862478
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 5, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 5, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 45, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 45, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 45, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '2160.dm.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': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 30, 'characteristic': True, 'core_order': 72, 'counter': 123, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2160.dm.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 168862495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 168862498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 168862502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 168862503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 36, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 168862504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 30, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 30, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 30, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862516
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 168862530
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 168862531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.36.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': True, 'core_order': 54, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 168862535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 54, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 54, 'counter': 161, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 27, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': 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: 168862538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 27, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.40.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': 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: 168862539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.40.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 45, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 15, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 15, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': False, 'core_order': 5, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': False, 'core_order': 5, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 168862551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 36, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 36, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.60.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 36, 'counter': 181, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 168862559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 9, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 9, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 18, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 6, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 6, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 6, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 6, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 9, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 9, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 168862581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 18, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 18, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 168862585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 18, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 168862586
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 360, 'characteristic': True, 'core_order': 30, 'counter': 206, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2160.dm.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 207, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862588
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 208, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 15, 'counter': 209, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 15, 'counter': 210, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 212, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862596
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862597
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 5, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 15, 'counter': 217, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862599
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862600
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 220, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 221, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 168862604
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862605
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862606
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862607
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862608
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862609
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862610
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 15, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862611
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862613
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862614
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862615
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.72.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': True, 'core_order': 27, 'counter': 233, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '2160.dm.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 168862617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 168862621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': 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: 168862624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': 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: 168862625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': 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: 168862626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.90.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 168862627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 5, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862633
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.108.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862637
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 168862638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 168862639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 18, 'counter': 254, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 6, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 6, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 3, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 9, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 9, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': 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: 168862661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 9, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '2160.dm.135.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '135.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': 135, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 168862670
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1080, 'characteristic': True, 'core_order': 15, 'counter': 282, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2160.dm.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 5, 'counter': 283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 5, 'counter': 284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.144.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862673
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 5, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862674
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 5, 'counter': 286, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.144.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 168862675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 6, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 310, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862703
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.180.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 168862706
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 5, 'counter': 314, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862707
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 5, 'counter': 315, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862708
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 5, 'counter': 316, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.216.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862709
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 5, 'counter': 317, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862710
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 318, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 319, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 5, 'counter': 320, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 168862714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 9, 'counter': 321, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2160.dm.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.169', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 169, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}:D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], '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: 168862715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 3, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 168862716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 3, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.240.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 168862717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 168862718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 135, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 168862719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 168862721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.270.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 168862727
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 360, 'characteristic': True, 'core_order': 6, 'counter': 333, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2160.dm.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '360.132', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 132, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 360, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862729
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862730
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 336, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862731
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 337, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862732
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862735
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862736
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862737
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862738
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862739
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 3, 'counter': 344, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862740
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862741
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862742
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862743
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.360.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862744
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862746
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862747
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862748
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862749
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862750
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862751
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 3, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862752
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862753
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862754
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862755
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.360.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 168862757
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': True, 'core_order': 5, 'counter': 360, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '2160.dm.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.741', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 741, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^3:C_2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 168862758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862764
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2160.dm.540.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862768
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.540.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862769
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.540.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 168862770
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1080, 'characteristic': True, 'core_order': 3, 'counter': 372, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2160.dm.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '720.808', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 808, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 720, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{10}\\times \\SOPlus(4,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 168862771
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 168862772
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.720.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 168862773
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 168862774
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.720.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 168862775
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862776
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862777
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862779
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862780
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862781
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862782
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2160.dm.1080.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, '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: 168862783
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2160.dm', 'ambient_counter': 91, 'ambient_order': 2160, 'ambient_tex': 'S_3^3:C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': True, 'core_order': 1, 'counter': 384, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2160.dm.2160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2160.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '2160.dm', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5240928682237879649, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^3:C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', '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: 168862736
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '120.d1.b1', '120.f1.b1', '180.h1.b1'], 'contains': ['720.c1.b1', '1080.b1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9475, -1, 5475, -1, 8732, -1, 6228, -1], 'generators': [334262, 151913], 'label': '2160.dm.360.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '360.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862467
    {'ambient': '2160.dm', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['2160.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '5.a1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1567, 4051, 8752, 4995, 2048, 4645, 7858, 4413], 'generators': [54, 333513, 160649, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862468
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.d1.a1', '12.g1.a1', '12.g1.b1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3968, 8095, 6006, 1815, 4675, 523, 4702, 410], 'generators': [54, 333513, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '432.741', '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': '432.741'}
  • id: 168862469
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.e1.b1', '12.h1.b1', '12.l1.b1'], 'contains': ['48.b1.b1', '72.c1.b1', '72.d1.b1', '72.e1.b1', '120.d1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8762, -1, 4907, -1, 7348, -1, 5334, -1], 'generators': [25866086400, 298233, 30, 160673], 'label': '2160.dm.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.d1.b1', 'projective_image': '432.741', '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': '4.2'}
  • id: 168862470
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.f1.a1', '12.i1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '72.c1.a1', '72.f1.a1', '120.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7451, -1, 964, -1, 6402, -1, 1813, -1], 'generators': [25866086400, 30, 328472, 288152], 'label': '2160.dm.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862471
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.f1.b1', '12.i1.b1', '12.l1.b1'], 'contains': ['48.b1.b1', '72.c1.b1', '72.f1.b1', '120.e1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7451, -1, 4542, -1, 6402, -1, 5439, -1], 'generators': [25866086400, 30, 160673, 338552], 'label': '2160.dm.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.e1.b1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862472
    {'ambient': '2160.dm', 'aut_centralizer_order': 9, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '72.e1.a1', '72.f1.a1', '120.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9668, -1, 44, -1, 9316, -1, 151, -1], 'generators': [25866086400, 338582, 328472, 288152], 'label': '2160.dm.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '24.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862473
    {'ambient': '2160.dm', 'aut_centralizer_order': 9, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '48.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.j1.b1'], 'contains': ['48.c1.b1', '72.e1.b1', '72.f1.b1', '120.f1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9668, -1, 5245, -1, 9316, -1, 4496, -1], 'generators': [288183, 25866086400, 151913, 338552], 'label': '2160.dm.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '24.f1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862474
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.c1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '72.d1.a1', '72.f1.a1', '120.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6929, -1, 2097, -1, 7697, -1, 728, -1], 'generators': [25866086400, 328472, 338552, 288152], 'label': '2160.dm.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862475
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.a1.b1', '12.c1.b1', '12.k1.b1'], 'contains': ['48.a1.a1', '72.d1.b1', '72.f1.b1', '120.g1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6929, -1, 5977, -1, 7697, -1, 5961, -1], 'generators': [25866086400, 160625, 328472, 338552], 'label': '2160.dm.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.g1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862476
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.g1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '72.g1.a1', '72.h1.a1', '120.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5025, -1, 3979, -1, 3884, -1, 3870, -1], 'generators': [333513, 25866086400, 30, 328472], 'label': '2160.dm.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.h1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862477
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.g1.b1', '12.l1.b1', '12.m1.b1'], 'contains': ['48.b1.b1', '72.g1.a1', '72.h1.b1', '120.h1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5025, -1, 7132, -1, 3884, -1, 6748, -1], 'generators': [333513, 25866086400, 298233, 30], 'label': '2160.dm.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.h1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862478
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.e1.a1', '12.i1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '72.i1.a1', '72.j1.a1', '120.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7908, -1, 1356, -1, 6999, -1, 1917, -1], 'generators': [288206, 25866086400, 30, 5760], 'label': '2160.dm.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.i1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862479
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8389', 'aut_weyl_index': 6, 'centralizer': '144.a1.a1', 'complements': ['540.c1.b1', '540.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '12.a1.a1', '12.l1.a1', '20.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4195, 4169, 7215, 8473, 3877, 5451, 3686, 4546], 'generators': [333513, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.b1.a1', '12.a1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862480
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.e1.b1', '12.i1.b1', '12.m1.b1'], 'contains': ['48.b1.b1', '72.i1.b1', '72.j1.b1', '120.i1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7908, -1, 4808, -1, 6999, -1, 5020, -1], 'generators': [160649, 25866086400, 298233, 30], 'label': '2160.dm.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.i1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862481
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '72.i1.a1', '72.l1.a1', '120.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9422, -1, 247, -1, 9488, -1, 255, -1], 'generators': [288206, 25866086400, 328502, 5760], 'label': '2160.dm.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.j1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862482
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.j1.b1'], 'contains': ['48.c1.b1', '72.i1.b1', '72.l1.b1', '120.j1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9422, -1, 4209, -1, 9488, -1, 4287, -1], 'generators': [160649, 288183, 25866086400, 298233], 'label': '2160.dm.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '24.j1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862483
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.a1', '12.k1.a1', '12.n1.a1'], 'contains': ['48.a1.a1', '72.i1.a1', '72.k1.a1', '120.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7096, -1, 1999, -1, 8240, -1, 832, -1], 'generators': [288206, 25866086400, 328472, 338552], 'label': '2160.dm.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862484
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.c1.b1', '12.k1.b1', '12.n1.b1'], 'contains': ['48.a1.a1', '72.i1.b1', '72.k1.b1', '120.k1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7096, -1, 5878, -1, 8240, -1, 5648, -1], 'generators': [160649, 25866086400, 328472, 338552], 'label': '2160.dm.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '24.k1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862485
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.f1.a1', '12.h1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '120.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8276, -1, 1094, -1, 7523, -1, 1305, -1], 'generators': [288206, 25866086400, 30, 328472], 'label': '2160.dm.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862486
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.f1.b1', '12.h1.b1', '12.m1.b1'], 'contains': ['48.b1.b1', '72.j1.b1', '72.k1.b1', '72.l1.b1', '120.l1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8276, -1, 4670, -1, 7523, -1, 4915, -1], 'generators': [160649, 25866086400, 30, 338552], 'label': '2160.dm.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.l1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862487
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.b1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '120.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8448, -1, 1545, -1, 8501, -1, 2076, -1], 'generators': [333567, 25866086400, 30, 328472], 'label': '2160.dm.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.m1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862488
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.b1', '12.h1.b1', '12.i1.b1'], 'contains': ['48.b1.b1', '72.m1.a1', '72.n1.b1', '72.o1.b1', '120.m1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8448, -1, 3858, -1, 8501, -1, 4081, -1], 'generators': [333567, 25866086400, 298233, 30], 'label': '2160.dm.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.m1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862489
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '72.n1.a1', '72.o1.a1', '72.o1.b1', '120.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9227, -1, 426, -1, 9921, -1, 622, -1], 'generators': [333567, 25866086400, 338582, 328472], 'label': '2160.dm.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.n1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862490
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8389', 'aut_weyl_index': 6, 'centralizer': '144.a1.a1', 'complements': ['540.c1.a1', '540.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.b1.a1', '8.d1.b1', '12.a1.b1', '12.l1.b1', '20.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4195, 4169, 7981, 7472, 3877, 5451, 7018, 7108], 'generators': [333513, 25866086400, 30, 328472, 160673, 338552], 'label': '2160.dm.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.b1.a1', '12.a1.b1', '20.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862491
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.j1.b1'], 'contains': ['48.c1.b1', '72.n1.b1', '72.o1.a1', '72.o1.b1', '120.n1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9227, -1, 3468, -1, 9921, -1, 3361, -1], 'generators': [333567, 288183, 25866086400, 298233], 'label': '2160.dm.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '24.n1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862492
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['48.a1.a1', '72.n1.a1', '72.n1.b1', '120.o1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7660, -1, 2841, -1, 8970, -1, 3468, -1], 'generators': [333567, 25866086400, 328472, 338552], 'label': '2160.dm.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862493
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.25', 'aut_weyl_index': 108, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1', '54.a1.b1', '54.b1.a1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '54.e1.a1', '135.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [533, -1, 9355, -1, 943, -1, 7926, -1], 'generators': [54, 288872, 25866086400, 160679, 288152], 'label': '2160.dm.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '432.741', '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: 168862494
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': ['72.j1.a1', '72.l1.a1', '72.a1.a1', '72.m1.a1', '72.o1.a1', '72.o1.b1', '72.j1.b1', '72.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.a1.b1', '60.b1.a1', '270.d1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1374, 1753, 9209, 8233, 1563, 8735, 9122, 8937], 'generators': [333513, 160625, 328472, 338552, 288152], 'label': '2160.dm.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.d1.a1'], 'normal_contains': ['60.a1.a1', '60.a1.b1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862495
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.d1.a1', '60.k1.a1', '60.n1.a1', '90.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3582, -1, 6326, -1, 4590, -1, 3381, -1], 'generators': [54, 333513, 328472, 338552, 288152], 'label': '2160.dm.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862496
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.a1.b1', '15.a1.a1'], 'contains': ['60.a1.b1', '60.c1.b1', '60.d1.a1', '60.k1.b1', '60.n1.b1', '90.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3582, -1, 7702, -1, 4590, -1, 7480, -1], 'generators': [54, 333513, 160679, 328472, 338552], 'label': '2160.dm.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862497
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.d1.a1', '60.o1.a1', '270.b1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1908, -1, 8920, -1, 1958, -1, 9334, -1], 'generators': [54, 120359, 333513, 328472, 338552], 'label': '2160.dm.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862498
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.a1.a1'], 'contains': ['60.e1.a1', '60.f1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1', '60.l1.a1', '60.m1.a1', '90.a1.a1', '90.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4433, -1, 3239, -1, 4755, -1, 2916, -1], 'generators': [54, 333513, 30, 328472, 288152], 'label': '2160.dm.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '30.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862499
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '10.a1.b1'], 'contains': ['60.e1.b1', '60.f1.b1', '60.g1.b1', '60.h1.b1', '60.i1.b1', '60.l1.b1', '60.m1.b1', '90.a1.b1', '90.b1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4433, -1, 6963, -1, 4755, -1, 7379, -1], 'generators': [54, 160649, 298233, 30, 5041], 'label': '2160.dm.30.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '30.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862500
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.n1.b1', '60.o1.a1', '270.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2404, -1, 8444, -1, 2565, -1, 8572, -1], 'generators': [333513, 160649, 328472, 338552, 288152], 'label': '2160.dm.30.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862501
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['540.a1.b1', '540.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '12.m1.a1', '12.n1.a1', '20.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3442, 5400, 7715, 4130, 3593, 3972, 4035, 5271], 'generators': [288206, 333513, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862502
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '10.c1.b1', '15.a1.a1'], 'contains': ['60.a1.b1', '60.n1.a1', '60.o1.a1', '270.c1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2404, -1, 8767, -1, 2565, -1, 9024, -1], 'generators': [333513, 160625, 120329, 328472, 338552], 'label': '2160.dm.30.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862503
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '10.e1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.n1.a1', '60.n1.b1', '270.e1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1176, -1, 9486, -1, 1402, -1, 8927, -1], 'generators': [288206, 333513, 160679, 328472, 338552], 'label': '2160.dm.30.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862504
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.i1.a1', '108.a1.a1', '180.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5559, -1, 1830, -1, 6057, -1, 1042, -1], 'generators': [54, 25866086400, 5760, 288152], 'label': '2160.dm.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '432.741', '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: 168862505
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.e1.b1', '18.a1.b1'], 'contains': ['72.b1.b1', '72.d1.b1', '72.i1.b1', '108.a1.b1', '180.a1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5559, -1, 5319, -1, 6057, -1, 6066, -1], 'generators': [54, 25866086400, 298233, 160679], 'label': '2160.dm.36.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.a1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862506
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.f1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.k1.a1', '108.a1.a1', '180.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5390, -1, 1713, -1, 6230, -1, 937, -1], 'generators': [54, 25866086400, 328472, 288152], 'label': '2160.dm.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862507
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.f1.b1', '18.a1.b1'], 'contains': ['72.b1.b1', '72.f1.b1', '72.k1.b1', '108.a1.b1', '180.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5390, -1, 5464, -1, 6230, -1, 5857, -1], 'generators': [54, 25866086400, 160679, 338552], 'label': '2160.dm.36.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '36.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862508
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.h1.a1', '72.n1.a1', '108.b1.a1', '180.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3944, -1, 2938, -1, 4828, -1, 2944, -1], 'generators': [54, 333513, 25866086400, 328472], 'label': '2160.dm.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862509
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.b1', '18.a1.b1'], 'contains': ['72.b1.b1', '72.h1.b1', '72.n1.b1', '108.b1.a1', '180.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3944, -1, 6449, -1, 4828, -1, 4809, -1], 'generators': [54, 333513, 25866086400, 298233], 'label': '2160.dm.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862510
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.j1.a1', '108.a1.a1', '180.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6205, -1, 1407, -1, 5568, -1, 2735, -1], 'generators': [54, 25866086400, 30, 288152], 'label': '2160.dm.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862511
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.f1.b1', '18.b1.b1'], 'contains': ['72.a1.a1', '72.c1.b1', '72.j1.b1', '108.a1.b1', '180.d1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6205, -1, 4394, -1, 5568, -1, 5544, -1], 'generators': [54, 160649, 25866086400, 30], 'label': '2160.dm.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.d1.b1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862512
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['540.c1.a1', '540.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.e1.b1', '12.m1.b1', '12.n1.b1', '20.c1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3442, 5400, 7571, 6586, 3593, 3972, 6861, 3522], 'generators': [333513, 160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '20.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862513
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.g1.b1', '18.b1.a1', '18.b1.b1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.g1.a1', '72.m1.a1', '108.b1.a1', '180.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2753, -1, 6281, -1, 2761, -1, 4600, -1], 'generators': [54, 333513, 25866086400, 30], 'label': '2160.dm.36.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862514
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.i1.a1', '18.b1.a1'], 'contains': ['72.c1.a1', '72.j1.a1', '72.m1.a1', '108.c1.a1', '180.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8812, -1, 642, -1, 6661, -1, 2182, -1], 'generators': [333567, 25866086400, 328473, 30], 'label': '2160.dm.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.a1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862515
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.i1.b1', '18.b1.b1'], 'contains': ['72.c1.b1', '72.j1.b1', '72.m1.a1', '108.c1.b1', '180.f1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8812, -1, 4750, -1, 6661, -1, 5125, -1], 'generators': [333567, 25866086400, 45329, 30], 'label': '2160.dm.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.b1', 'old_label': '36.f1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862516
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.k1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '72.k1.a1', '72.n1.a1', '108.c1.a1', '180.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7766, -1, 1529, -1, 8796, -1, 517, -1], 'generators': [333567, 25866086400, 328473, 5760], 'label': '2160.dm.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '432.741', '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: 168862517
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.k1.b1', '18.a1.b1'], 'contains': ['72.d1.b1', '72.k1.b1', '72.n1.b1', '108.c1.b1', '180.g1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7766, -1, 5953, -1, 8796, -1, 5752, -1], 'generators': [333567, 25866086400, 160679, 338552], 'label': '2160.dm.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.g1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862518
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.j1.a1'], 'contains': ['72.e1.a1', '72.l1.a1', '72.o1.a1', '108.c1.a1', '180.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9847, -1, 89, -1, 9747, -1, 46, -1], 'generators': [333567, 25866086400, 328473, 5790], 'label': '2160.dm.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '36.h1.a1', 'projective_image': '432.741', '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: 168862519
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.j1.b1'], 'contains': ['72.e1.b1', '72.l1.b1', '72.o1.b1', '108.c1.b1', '180.h1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9847, -1, 4849, -1, 9747, -1, 4392, -1], 'generators': [333567, 160649, 293943, 25866086400], 'label': '2160.dm.36.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.b1', 'old_label': '36.h1.b1', 'projective_image': '432.741', '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: 168862520
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.b1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.c1.a1', '72.g1.a1', '108.d1.a1', '180.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2231, -1, 7809, -1, 2251, -1, 6171, -1], 'generators': [288872, 25866086400, 30, 288152], 'label': '2160.dm.36.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '432.741', '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': '4.2'}
  • id: 168862521
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '18.b1.b1', '18.d1.b1', '18.e1.a1'], 'contains': ['72.c1.b1', '72.g1.a1', '108.d1.b1', '180.i1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2231, -1, 8467, -1, 2251, -1, 8091, -1], 'generators': [288872, 25866086400, 30, 160673], 'label': '2160.dm.36.i1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.b1', 'projective_image': '432.741', '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': '4.2'}
  • id: 168862522
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.j1.a1', '12.k1.a1', '18.a1.a1'], 'contains': ['72.f1.a1', '72.i1.a1', '72.n1.a1', '108.c1.a1', '180.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8980, -1, 809, -1, 9144, -1, 412, -1], 'generators': [333567, 25866086400, 328472, 288152], 'label': '2160.dm.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '432.741', '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: 168862523
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.93925', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': ['540.c1.a1', '540.a1.a1', '540.c1.b1', '540.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '12.b1.a1', '20.d1.a1', '36.m1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1075, 2114, 9316, 5606, 1404, 7340, 8714, 7914], 'generators': [333513, 120353, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '12.b1.a1', '20.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862524
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.j1.b1', '12.k1.b1', '18.a1.b1'], 'contains': ['72.f1.b1', '72.i1.b1', '72.n1.b1', '108.c1.b1', '180.j1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8980, -1, 5608, -1, 9144, -1, 5229, -1], 'generators': [333567, 25866086400, 298233, 151919], 'label': '2160.dm.36.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.j1.b1', 'projective_image': '432.741', '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: 168862525
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.l1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.h1.a1', '108.d1.a1', '180.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4908, -1, 2840, -1, 4056, -1, 2286, -1], 'generators': [333513, 25866086400, 328472, 288152], 'label': '2160.dm.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.k1.a1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862526
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.l1.b1', '18.a1.b1'], 'contains': ['72.d1.b1', '72.f1.b1', '72.h1.b1', '108.d1.b1', '180.k1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4908, -1, 7290, -1, 4056, -1, 7128, -1], 'generators': [25866086400, 298233, 160625, 5041], 'label': '2160.dm.36.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.k1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862527
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.b1.a1', '18.d1.b1', '18.f1.a1'], 'contains': ['72.g1.a1', '72.j1.a1', '108.e1.a1', '180.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2022, -1, 7663, -1, 2424, -1, 6276, -1], 'generators': [288206, 288872, 25866086400, 30], 'label': '2160.dm.36.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862528
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '18.b1.b1', '18.d1.a1', '18.f1.a1'], 'contains': ['72.g1.a1', '72.j1.b1', '108.e1.b1', '180.l1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2022, -1, 8299, -1, 2424, -1, 7986, -1], 'generators': [288872, 160649, 25866086400, 30], 'label': '2160.dm.36.l1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.l1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862529
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '18.c1.a1', '18.e1.a1', '18.f1.a1'], 'contains': ['72.g1.a1', '108.f1.a1', '180.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [252, -1, 9903, -1, 504, -1, 9208, -1], 'generators': [288872, 120353, 25866086400, 30], 'label': '2160.dm.36.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.m1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862530
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '18.c1.a1', '18.d1.a1', '18.d1.b1'], 'contains': ['72.g1.a1', '108.g1.a1', '180.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1499, -1, 9027, -1, 1719, -1, 8996, -1], 'generators': [288872, 25866086400, 120329, 30], 'label': '2160.dm.36.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862531
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.n1.a1', '18.a1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.k1.a1', '108.e1.a1', '180.o1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4190, -1, 4095, -1, 4228, -1, 2631, -1], 'generators': [288206, 333513, 25866086400, 328472], 'label': '2160.dm.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.o1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862532
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '12.n1.b1', '18.a1.b1'], 'contains': ['72.h1.b1', '72.i1.b1', '72.k1.b1', '108.e1.b1', '180.o1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4190, -1, 6823, -1, 4228, -1, 6905, -1], 'generators': [160649, 25866086400, 298233, 5041], 'label': '2160.dm.36.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.o1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862533
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.120', 'aut_weyl_index': 36, 'centralizer': '48.a1.a1', 'complements': ['54.c1.b1', '54.d1.a1', '54.c1.a1', '54.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.f1.a1', '20.f1.b1'], 'contains': ['80.a1.a1', '120.b1.a1', '120.c1.a1', '120.c1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4992, 8656, 3475, 1003, 4997, 1230, 4185, 1401], 'generators': [54, 30, 328472, 338552], 'label': '2160.dm.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '360.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '8.3', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 168862534
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': ['540.c1.a1', '540.a1.a1', '540.c1.b1', '540.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.b1.a1', '12.o1.a1', '20.e1.a1', '36.n1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2354, 6513, 8384, 3173, 2863, 1630, 8322, 2003], 'generators': [333513, 25866086400, 120329, 30, 328472, 338552], 'label': '2160.dm.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.b1.a1', '20.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862535
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '40.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1', '20.b1.a1', '20.b1.b1', '20.c1.a1', '20.c1.b1', '20.d1.a1', '20.e1.a1'], 'contains': ['80.a1.a1', '120.a1.a1', '120.h1.a1', '120.h1.b1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3134, 5781, 8045, 5095, 3131, 4061, 7500, 4358], 'generators': [333513, 30, 328472, 338552], 'label': '2160.dm.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.a1', '20.b1.a1', '20.b1.b1', '20.c1.b1', '20.c1.a1', '20.d1.a1', '20.e1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862536
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '40.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['54.c1.b1', '54.d1.a1', '54.c1.a1', '54.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.a1.a1', '20.g1.a1', '20.g1.b1'], 'contains': ['80.a1.a1', '120.m1.a1', '120.m1.b1', '120.n1.a1', '120.n1.b1', '120.o1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6594, 7582, 4086, 1924, 8650, 2733, 3663, 2580], 'generators': [333567, 30, 328472, 338552], 'label': '2160.dm.40.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': ['8.c1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '8.3', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862537
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.b1.a1', '20.f1.a1', '20.g1.a1'], 'contains': ['80.a1.a1', '120.d1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6309, -1, 2442, -1, 6830, -1, 1604, -1], 'generators': [30, 328472, 338552, 288152], 'label': '2160.dm.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862538
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '48.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '20.b1.b1', '20.f1.b1', '20.g1.b1'], 'contains': ['80.a1.a1', '120.d1.b1', '120.e1.b1', '120.f1.b1', '120.g1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6309, -1, 6091, -1, 6830, -1, 7604, -1], 'generators': [30, 328472, 160673, 338552], 'label': '2160.dm.40.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '40.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862539
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '20.c1.a1', '20.f1.a1', '20.g1.a1'], 'contains': ['80.a1.a1', '120.i1.a1', '120.j1.a1', '120.k1.a1', '120.l1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5906, -1, 2276, -1, 7173, -1, 1707, -1], 'generators': [288206, 30, 328472, 338552], 'label': '2160.dm.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862540
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '20.c1.b1', '20.f1.b1', '20.g1.b1'], 'contains': ['80.a1.a1', '120.i1.b1', '120.j1.b1', '120.k1.b1', '120.l1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5906, -1, 6602, -1, 7173, -1, 7234, -1], 'generators': [160649, 30, 328472, 338552], 'label': '2160.dm.40.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '40.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862541
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '9.a1.a1'], 'contains': ['90.b1.a1', '90.b1.b1', '90.c1.a1', '90.d1.a1', '90.d1.b1', '90.e1.a1', '90.f1.a1', '135.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [918, -1, 9719, -1, 277, -1, 9618, -1], 'generators': [54, 288872, 160649, 30, 288152], 'label': '2160.dm.45.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862542
    {'ambient': '2160.dm', 'aut_centralizer_order': 54, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.119', 'aut_weyl_index': 54, 'centralizer': '8.a1.a1', 'complements': ['45.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.g1.a1', '24.g1.b1', '24.k1.a1', '24.k1.b1', '24.o1.a1'], 'contains': ['144.b1.a1', '144.b1.b1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7280, 7261, 2813, 2200, 7540, 2808, 3997, 2639], 'generators': [25866086400, 328472, 338552], 'label': '2160.dm.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['240.a1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '8.3', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 168862543
    {'ambient': '2160.dm', 'aut_centralizer_order': 54, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.h1.a1', '24.i1.a1', '24.l1.a1', '24.m1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '240.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8248, -1, 1056, -1, 7272, -1, 2725, -1], 'generators': [25866086400, 30, 328472], 'label': '2160.dm.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862544
    {'ambient': '2160.dm', 'aut_centralizer_order': 54, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.b1', '24.d1.b1', '24.e1.b1', '24.h1.b1', '24.i1.b1', '24.l1.b1', '24.m1.b1'], 'contains': ['144.a1.a1', '144.b1.b1', '144.c1.b1', '240.b1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8248, -1, 3841, -1, 7272, -1, 4917, -1], 'generators': [25866086400, 298233, 30], 'label': '2160.dm.48.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862545
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.950', 'aut_weyl_index': 12, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1', '20.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5954, -1, 2214, -1, 6050, -1, 2464, -1], 'generators': [54, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.4.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': '4.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862546
    {'ambient': '2160.dm', 'aut_centralizer_order': 27, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.f1.a1', '24.j1.a1', '24.n1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.c1.b1', '240.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9600, -1, 273, -1, 9138, -1, 1341, -1], 'generators': [25866086400, 338582, 328472], 'label': '2160.dm.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '48.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862547
    {'ambient': '2160.dm', 'aut_centralizer_order': 27, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.f1.b1', '24.j1.b1', '24.n1.b1'], 'contains': ['144.b1.b1', '144.c1.a1', '144.c1.b1', '240.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9600, -1, 3420, -1, 9138, -1, 3805, -1], 'generators': [288183, 25866086400, 298233], 'label': '2160.dm.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '48.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862548
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '270.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2692, -1, 6433, -1, 2945, -1, 3759, -1], 'generators': [54, 288872, 25866086400, 288152], 'label': '2160.dm.54.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862549
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '18.b1.b1', '27.a1.a1'], 'contains': ['108.a1.b1', '108.b1.a1', '108.c1.b1', '108.d1.b1', '108.e1.b1', '270.a1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2692, -1, 7837, -1, 2945, -1, 7017, -1], 'generators': [54, 288872, 25866086400, 160679], 'label': '2160.dm.54.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862550
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '18.c1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.g1.a1', '270.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [682, -1, 9574, -1, 864, -1, 9127, -1], 'generators': [54, 288872, 120359, 25866086400], 'label': '2160.dm.54.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862551
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '18.d1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.e1.b1', '108.g1.a1', '270.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1790, -1, 8855, -1, 2092, -1, 8633, -1], 'generators': [288872, 160649, 25866086400, 288152], 'label': '2160.dm.54.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862552
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '18.d1.b1', '27.a1.a1'], 'contains': ['108.d1.b1', '108.e1.a1', '108.g1.a1', '270.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1790, -1, 9031, -1, 2092, -1, 8810, -1], 'generators': [288872, 25866086400, 160625, 120329], 'label': '2160.dm.54.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862553
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.25', 'aut_weyl_index': 108, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.d1.b1', '108.f1.a1', '270.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [265, -1, 9483, -1, 1023, -1, 8898, -1], 'generators': [288872, 25866086400, 160625, 288152], 'label': '2160.dm.54.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862554
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.25', 'aut_weyl_index': 108, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.e1.a1', '108.e1.b1', '108.f1.a1', '270.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [447, -1, 9895, -1, 1168, -1, 8721, -1], 'generators': [288206, 288872, 25866086400, 160679], 'label': '2160.dm.54.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862555
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': ['36.f1.b1', '36.h1.b1', '36.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.b1.a1', '30.a1.a1', '30.b1.a1', '30.e1.a1'], 'contains': ['120.a1.a1', '120.g1.a1', '180.k1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3201, 3324, 7245, 8005, 3348, 5583, 3281, 7130], 'generators': [333513, 328472, 338552, 288152], 'label': '2160.dm.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.b1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862556
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.950', 'aut_weyl_index': 12, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '8.d1.b1', '8.e1.b1', '12.c1.b1', '12.e1.b1', '12.f1.b1', '20.f1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5954, -1, 4694, -1, 6050, -1, 5597, -1], 'generators': [54, 160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.f1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862557
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': ['36.f1.a1', '36.h1.a1', '36.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.b1.b1', '30.a1.a1', '30.b1.b1', '30.e1.b1'], 'contains': ['120.a1.a1', '120.g1.b1', '180.k1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3201, 3324, 8361, 8603, 3348, 5583, 8563, 7566], 'generators': [333513, 160625, 328472, 338552], 'label': '2160.dm.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['12.a1.b1', '20.b1.b1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862575
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '20.g1.a1', '30.b1.a1'], 'contains': ['120.g1.a1', '120.k1.a1', '120.o1.a1', '180.g1.a1', '180.j1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6720, -1, 2456, -1, 8369, -1, 1120, -1], 'generators': [333567, 328472, 338552, 288152], 'label': '2160.dm.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.k1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862558
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': ['36.f1.a1', '36.h1.a1', '36.d1.a1', '36.f1.b1', '36.h1.b1', '36.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.d1.a1', '30.a1.a1', '30.c1.a1', '30.f1.a1'], 'contains': ['120.a1.a1', '540.f1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1341, 2189, 9248, 6970, 1387, 7077, 9403, 8117], 'generators': [120305, 333513, 328472, 338552], 'label': '2160.dm.60.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.b1.a1', 'normal_contained_in': ['12.b1.a1', '20.d1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862559
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.f1.a1', '30.b1.a1'], 'contains': ['120.b1.a1', '120.g1.a1', '120.k1.a1', '180.a1.a1', '180.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5656, -1, 2721, -1, 5726, -1, 1403, -1], 'generators': [54, 328472, 338552, 288152], 'label': '2160.dm.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862560
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '20.f1.b1', '30.b1.b1'], 'contains': ['120.b1.a1', '120.g1.b1', '120.k1.b1', '180.a1.b1', '180.b1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5656, -1, 5702, -1, 5726, -1, 7890, -1], 'generators': [54, 160679, 328472, 338552], 'label': '2160.dm.60.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '60.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862561
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.a1.a1', '30.b1.a1', '30.b1.b1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.o1.a1', '180.c1.a1', '180.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3488, -1, 7635, -1, 4489, -1, 6589, -1], 'generators': [54, 333513, 328472, 338552], 'label': '2160.dm.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862562
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.f1.a1', '30.d1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.i1.a1', '180.a1.a1', '180.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5390, -1, 2637, -1, 5152, -1, 2535, -1], 'generators': [54, 30, 5760, 288152], 'label': '2160.dm.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862563
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '20.f1.b1', '30.d1.b1'], 'contains': ['120.c1.b1', '120.d1.b1', '120.i1.b1', '180.a1.b1', '180.d1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5390, -1, 4994, -1, 5152, -1, 7751, -1], 'generators': [54, 160649, 298233, 30], 'label': '2160.dm.60.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862564
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '20.f1.a1', '30.d1.a1'], 'contains': ['120.c1.a1', '120.e1.a1', '120.l1.a1', '180.b1.a1', '180.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5519, -1, 2555, -1, 5267, -1, 2465, -1], 'generators': [54, 30, 328472, 288152], 'label': '2160.dm.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862565
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '20.f1.b1', '30.d1.b1'], 'contains': ['120.c1.b1', '120.e1.b1', '120.l1.b1', '180.b1.b1', '180.d1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5519, -1, 5107, -1, 5267, -1, 7681, -1], 'generators': [54, 160649, 30, 338552], 'label': '2160.dm.60.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '60.f1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862566
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '20.a1.a1', '30.d1.a1'], 'contains': ['120.c1.a1', '120.h1.a1', '120.m1.a1', '180.c1.a1', '180.e1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3703, -1, 3284, -1, 4357, -1, 3949, -1], 'generators': [54, 333513, 30, 328472], 'label': '2160.dm.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862567
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4367', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '20.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7659, -1, 1953, -1, 7681, -1, 1742, -1], 'generators': [333567, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.4.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': '4.g1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 168862568
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '20.a1.a1', '30.d1.b1'], 'contains': ['120.c1.b1', '120.h1.b1', '120.m1.b1', '180.c1.b1', '180.e1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3703, -1, 6903, -1, 4357, -1, 6826, -1], 'generators': [54, 333513, 298233, 30], 'label': '2160.dm.60.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.g1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862569
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '20.g1.a1', '30.d1.a1'], 'contains': ['120.d1.a1', '120.l1.a1', '120.m1.a1', '180.f1.a1', '180.g1.a1', '180.h1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6474, -1, 2100, -1, 7871, -1, 1500, -1], 'generators': [333567, 328473, 30, 5760], 'label': '2160.dm.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.h1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862570
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '20.g1.b1', '30.d1.b1'], 'contains': ['120.d1.b1', '120.l1.b1', '120.m1.b1', '180.f1.b1', '180.g1.b1', '180.h1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6474, -1, 6682, -1, 7871, -1, 7341, -1], 'generators': [333567, 160649, 30, 338552], 'label': '2160.dm.60.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.h1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862571
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '20.g1.a1', '30.d1.a1'], 'contains': ['120.e1.a1', '120.i1.a1', '120.m1.a1', '180.f1.a1', '180.j1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6345, -1, 2221, -1, 6532, -1, 1996, -1], 'generators': [333567, 30, 328472, 288152], 'label': '2160.dm.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.i1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862572
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '20.g1.b1', '30.d1.b1'], 'contains': ['120.e1.b1', '120.i1.b1', '120.m1.b1', '180.f1.b1', '180.j1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6345, -1, 6567, -1, 6532, -1, 7421, -1], 'generators': [151889, 333567, 298233, 30], 'label': '2160.dm.60.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.i1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862573
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '20.g1.a1'], 'contains': ['120.f1.a1', '120.j1.a1', '120.n1.a1', '180.h1.a1', '180.j1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9244, -1, 437, -1, 9618, -1, 334, -1], 'generators': [333567, 338582, 328472, 288152], 'label': '2160.dm.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '60.j1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862574
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '20.g1.b1'], 'contains': ['120.f1.b1', '120.j1.b1', '120.n1.b1', '180.h1.b1', '180.j1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9244, -1, 6251, -1, 9618, -1, 6669, -1], 'generators': [333567, 160649, 298233, 328502], 'label': '2160.dm.60.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '60.j1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862576
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '20.g1.b1', '30.b1.b1'], 'contains': ['120.g1.b1', '120.k1.b1', '120.o1.a1', '180.g1.b1', '180.j1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6720, -1, 6826, -1, 8369, -1, 7820, -1], 'generators': [333567, 160679, 328472, 338552], 'label': '2160.dm.60.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '60.k1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862577
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '20.b1.a1', '30.d1.a1'], 'contains': ['120.d1.a1', '120.e1.a1', '120.h1.a1', '180.i1.a1', '180.k1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4411, -1, 3218, -1, 3640, -1, 3040, -1], 'generators': [333513, 30, 328472, 288152], 'label': '2160.dm.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.l1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862578
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['1080.b1.b1', '1080.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.f1.a1', '4.g1.a1', '6.b1.a1', '6.d1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4195, 5415, 6943, 3436, 4675, 3355, 3686, 4058], 'generators': [54, 333513, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '432.741', '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': '432.741'}
  • id: 168862579
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4367', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.c1.a1', '8.d1.b1', '8.e1.b1', '12.h1.b1', '12.i1.b1', '12.j1.b1', '12.k1.b1', '20.g1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7659, -1, 6153, -1, 7681, -1, 5292, -1], 'generators': [333567, 160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.g1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 168862580
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '20.b1.b1', '30.d1.b1'], 'contains': ['120.d1.b1', '120.e1.b1', '120.h1.b1', '180.i1.b1', '180.k1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4411, -1, 7544, -1, 3640, -1, 8441, -1], 'generators': [298233, 30, 160673, 5041], 'label': '2160.dm.60.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.l1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862581
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '20.c1.a1', '30.d1.a1'], 'contains': ['120.h1.a1', '120.i1.a1', '120.l1.a1', '180.l1.a1', '180.o1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3865, -1, 3870, -1, 3755, -1, 3109, -1], 'generators': [288206, 333513, 30, 328472], 'label': '2160.dm.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '60.m1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862582
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '20.c1.b1', '30.d1.b1'], 'contains': ['120.h1.b1', '120.i1.b1', '120.l1.b1', '180.l1.b1', '180.o1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3865, -1, 7069, -1, 3755, -1, 8271, -1], 'generators': [160649, 298233, 30, 5041], 'label': '2160.dm.60.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '60.m1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862583
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '20.c1.a1', '30.b1.a1', '30.e1.b1', '30.f1.a1'], 'contains': ['120.a1.a1', '120.k1.a1', '180.o1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2941, -1, 8410, -1, 3262, -1, 4001, -1], 'generators': [288206, 333513, 328472, 338552], 'label': '2160.dm.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.n1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862584
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.b1', '20.c1.b1', '30.b1.b1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.a1.a1', '120.k1.b1', '180.o1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2941, -1, 8203, -1, 3262, -1, 8511, -1], 'generators': [333513, 160649, 328472, 338552], 'label': '2160.dm.60.n1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.n1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862585
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '20.e1.a1', '30.c1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.a1.a1', '540.g1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2372, -1, 8664, -1, 1873, -1, 9325, -1], 'generators': [333513, 120329, 328472, 338552], 'label': '2160.dm.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862586
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '6.a1.a1', 'complements': ['30.e1.b1', '30.a1.a1', '30.e1.a1', '30.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.c1.b1', '36.d1.a1', '36.d1.b1', '36.e1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '360.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4608, 9469, 2942, 282, 5121, 542, 3901, 861], 'generators': [54, 25866086400, 30], 'label': '2160.dm.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['144.a1.a1', '360.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862587
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['144.b1.a1', '216.a1.a1', '360.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4921, -1, 1769, -1, 5605, -1, 2980, -1], 'generators': [54, 25866086400, 328472], 'label': '2160.dm.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862588
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.b1', '36.a1.b1', '36.b1.b1', '36.c1.b1'], 'contains': ['144.b1.b1', '216.a1.a1', '360.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4921, -1, 4761, -1, 5605, -1, 5002, -1], 'generators': [54, 25866086400, 298233], 'label': '2160.dm.72.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '72.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862589
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '36.d1.a1', '36.f1.a1', '36.i1.a1'], 'contains': ['144.a1.a1', '216.b1.a1', '360.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7935, -1, 687, -1, 6016, -1, 3037, -1], 'generators': [25866086400, 30, 288152], 'label': '2160.dm.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862590
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.a1.b1', '10.b1.a1', '10.c1.a1', '10.c1.b1', '10.d1.a1', '10.e1.a1', '15.a1.a1', '45.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1927, 3802, 8897, 4244, 1916, 5136, 8930, 4768], 'generators': [54, 333513, 160649, 30, 328472, 338552, 288152], 'label': '2160.dm.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.a1.b1', '10.b1.a1', '10.c1.a1', '10.c1.b1', '10.d1.a1', '10.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862591
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '24.e1.b1', '36.d1.b1', '36.f1.b1', '36.i1.b1'], 'contains': ['144.a1.a1', '216.b1.b1', '360.c1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7935, -1, 4573, -1, 6016, -1, 5309, -1], 'generators': [25866086400, 30, 160673], 'label': '2160.dm.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.c1.b1', 'projective_image': '432.741', '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': '2.1'}
  • id: 168862592
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.g1.a1', '36.a1.a1', '36.g1.a1', '36.k1.a1'], 'contains': ['144.b1.a1', '216.b1.a1', '360.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7307, -1, 1555, -1, 7406, -1, 1717, -1], 'generators': [25866086400, 5760, 288152], 'label': '2160.dm.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862593
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '24.g1.b1', '36.a1.b1', '36.g1.b1', '36.k1.b1'], 'contains': ['144.b1.b1', '216.b1.b1', '360.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7307, -1, 5858, -1, 7406, -1, 5645, -1], 'generators': [25866086400, 298233, 160625], 'label': '2160.dm.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.d1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862594
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.f1.a1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.b1.a1', '360.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9925, -1, 62, -1, 9004, -1, 952, -1], 'generators': [25866086400, 5790, 288152], 'label': '2160.dm.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862595
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '24.f1.b1', '36.h1.b1'], 'contains': ['144.c1.b1', '216.b1.b1', '360.e1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9925, -1, 4625, -1, 9004, -1, 4664, -1], 'generators': [25866086400, 334262, 151913], 'label': '2160.dm.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '72.e1.b1', 'projective_image': '432.741', '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': '2.1'}
  • id: 168862596
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.g1.a1', '36.b1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.b1.a1', '216.b1.a1', '360.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7721, -1, 1048, -1, 7841, -1, 1542, -1], 'generators': [25866086400, 328472, 288152], 'label': '2160.dm.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862597
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.g1.b1', '36.b1.b1', '36.j1.b1', '36.k1.b1'], 'contains': ['144.b1.b1', '216.b1.b1', '360.f1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7721, -1, 5495, -1, 7841, -1, 5469, -1], 'generators': [25866086400, 160625, 338552], 'label': '2160.dm.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '72.f1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862598
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.h1.b1', '36.e1.a1', '36.i1.a1', '36.i1.b1', '36.l1.a1', '36.l1.b1', '36.m1.a1', '36.n1.a1'], 'contains': ['144.a1.a1', '216.c1.a1', '360.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2184, -1, 8096, -1, 2603, -1, 6507, -1], 'generators': [333513, 25866086400, 30], 'label': '2160.dm.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.741', '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': '2.1'}
  • id: 168862599
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.h1.a1', '36.c1.a1', '36.k1.a1', '36.o1.a1'], 'contains': ['144.b1.a1', '216.c1.a1', '360.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4113, -1, 3788, -1, 4142, -1, 3705, -1], 'generators': [333513, 25866086400, 328472], 'label': '2160.dm.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.h1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862600
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.h1.b1', '36.c1.b1', '36.k1.b1', '36.o1.b1'], 'contains': ['144.b1.b1', '216.c1.a1', '360.h1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4113, -1, 7314, -1, 4142, -1, 6435, -1], 'generators': [333513, 25866086400, 298233], 'label': '2160.dm.72.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.h1.b1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862601
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['360.j1.a1', '360.l1.a1', '360.a1.a1', '360.m1.a1', '360.o1.b1', '360.o1.a1', '360.j1.b1', '360.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '30.a1.a1', '54.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1200, 531, 9119, 9324, 2142, 9508, 8175, 9614], 'generators': [333513, 25866086400, 160625, 328472, 338552, 288152], 'label': '2160.dm.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862602
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.j1.a1', '24.k1.a1', '36.a1.a1', '36.j1.a1', '36.o1.a1'], 'contains': ['144.b1.a1', '216.d1.a1', '360.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8105, -1, 962, -1, 8056, -1, 1614, -1], 'generators': [288206, 25866086400, 5760], 'label': '2160.dm.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '432.741', '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: 168862603
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.j1.b1', '24.k1.b1', '36.a1.b1', '36.j1.b1', '36.o1.b1'], 'contains': ['144.b1.b1', '216.d1.b1', '360.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8105, -1, 5377, -1, 8056, -1, 5147, -1], 'generators': [160649, 25866086400, 298233], 'label': '2160.dm.72.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '72.i1.b1', 'projective_image': '432.741', '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: 168862604
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.l1.a1', '36.d1.a1', '36.f1.a1', '36.l1.a1'], 'contains': ['144.a1.a1', '216.d1.a1', '360.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8424, -1, 848, -1, 6354, -1, 3109, -1], 'generators': [288206, 25866086400, 30], 'label': '2160.dm.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.j1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862605
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.l1.b1', '36.d1.b1', '36.f1.b1', '36.l1.b1'], 'contains': ['144.a1.a1', '216.d1.b1', '360.j1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8424, -1, 4504, -1, 6354, -1, 5075, -1], 'generators': [160649, 25866086400, 30], 'label': '2160.dm.72.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.j1.b1', 'projective_image': '432.741', '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': '6.1'}
  • id: 168862606
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.l1.a1', '36.b1.a1', '36.g1.a1', '36.o1.a1'], 'contains': ['144.b1.a1', '216.d1.a1', '360.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7423, -1, 1382, -1, 7698, -1, 1789, -1], 'generators': [288206, 25866086400, 328472], 'label': '2160.dm.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862607
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '36.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.l1.b1', '36.b1.b1', '36.g1.b1', '36.o1.b1'], 'contains': ['144.b1.b1', '216.d1.b1', '360.k1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7423, -1, 5768, -1, 7698, -1, 5381, -1], 'generators': [160649, 25866086400, 338552], 'label': '2160.dm.72.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '72.k1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862608
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.l1.a1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.d1.a1', '360.l1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9627, -1, 130, -1, 9296, -1, 1024, -1], 'generators': [288206, 25866086400, 328502], 'label': '2160.dm.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '72.l1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862609
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.l1.b1', '36.h1.b1'], 'contains': ['144.c1.b1', '216.d1.b1', '360.l1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9627, -1, 4237, -1, 9296, -1, 4508, -1], 'generators': [160649, 25866086400, 338582], 'label': '2160.dm.72.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '72.l1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862610
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.m1.b1', '36.e1.a1', '36.f1.a1', '36.f1.b1'], 'contains': ['144.a1.a1', '216.e1.a1', '360.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8748, -1, 3047, -1, 6498, -1, 3481, -1], 'generators': [333567, 25866086400, 30], 'label': '2160.dm.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.m1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862611
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.n1.a1', '24.o1.a1', '36.c1.a1', '36.g1.a1', '36.j1.a1'], 'contains': ['144.b1.a1', '216.e1.a1', '360.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8608, -1, 1262, -1, 8599, -1, 2069, -1], 'generators': [333567, 25866086400, 328472], 'label': '2160.dm.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.n1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862612
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.k1.a1', '12.n1.a1', '18.a1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3700, -1, 7011, -1, 4900, -1, 3381, -1], 'generators': [54, 333513, 25866086400, 328472, 338552, 288152], 'label': '2160.dm.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862613
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.n1.b1', '24.o1.a1', '36.c1.b1', '36.g1.b1', '36.j1.b1'], 'contains': ['144.b1.b1', '216.e1.a1', '360.n1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8608, -1, 4693, -1, 8599, -1, 4311, -1], 'generators': [333567, 25866086400, 298233], 'label': '2160.dm.72.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '72.n1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862614
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.n1.a1', '24.n1.b1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.e1.a1', '360.o1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9487, -1, 360, -1, 9613, -1, 1876, -1], 'generators': [333567, 25866086400, 328502], 'label': '2160.dm.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '72.o1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862615
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.n1.a1', '24.n1.b1', '36.h1.b1'], 'contains': ['144.c1.b1', '216.e1.a1', '360.o1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9487, -1, 3313, -1, 9613, -1, 3394, -1], 'generators': [333567, 25866086400, 338582], 'label': '2160.dm.72.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.b1', 'old_label': '72.o1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862616
    {'ambient': '2160.dm', 'aut_centralizer_order': 108, 'aut_label': '80.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '32.40', 'aut_weyl_index': 108, 'centralizer': '16.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1', '40.d1.a1', '40.d1.b1', '40.e1.a1', '40.e1.b1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.b1.b1', '240.c1.a1', '240.c1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6126, 8065, 3864, 1593, 6999, 2229, 4182, 2184], 'generators': [30, 328472, 338552], 'label': '2160.dm.80.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'normal_contains': ['240.a1.a1', '720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '16.11', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 168862617
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.b1.a1', '30.d1.a1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.c1.a1', '180.g1.a1', '180.j1.a1', '180.k1.a1', '180.o1.a1', '270.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4060, -1, 3172, -1, 4660, -1, 2388, -1], 'generators': [54, 333513, 328472, 288152], 'label': '2160.dm.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862618
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '30.b1.b1', '30.d1.b1'], 'contains': ['180.a1.b1', '180.b1.b1', '180.c1.b1', '180.g1.b1', '180.j1.b1', '180.k1.b1', '180.o1.b1', '270.a1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4060, -1, 7277, -1, 4660, -1, 8194, -1], 'generators': [54, 298233, 160679, 5041], 'label': '2160.dm.90.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '90.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862619
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.d1.a1', '45.a1.a1'], 'contains': ['180.d1.a1', '180.e1.a1', '180.f1.a1', '180.i1.a1', '180.l1.a1', '270.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2518, -1, 6607, -1, 2593, -1, 6379, -1], 'generators': [54, 288872, 30, 288152], 'label': '2160.dm.90.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862620
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '30.d1.b1', '45.a1.a1'], 'contains': ['180.d1.b1', '180.e1.a1', '180.f1.b1', '180.i1.b1', '180.l1.b1', '270.a1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2518, -1, 7952, -1, 2593, -1, 8347, -1], 'generators': [54, 288872, 160649, 30], 'label': '2160.dm.90.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862621
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '18.c1.a1', '45.a1.a1'], 'contains': ['180.e1.a1', '180.m1.a1', '180.n1.a1', '270.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [894, -1, 9431, -1, 291, -1, 9962, -1], 'generators': [54, 288872, 120329, 30], 'label': '2160.dm.90.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862622
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '18.d1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '180.l1.b1', '180.n1.a1', '270.c1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1462, -1, 8833, -1, 1581, -1, 9472, -1], 'generators': [288872, 160649, 30, 288152], 'label': '2160.dm.90.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862623
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.c1.b1', '12.d1.a1', '12.k1.b1', '12.n1.b1', '18.a1.b1', '30.b1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3700, -1, 7284, -1, 4900, -1, 6709, -1], 'generators': [54, 333513, 25866086400, 160679, 328472, 338552], 'label': '2160.dm.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862624
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.b1', '18.d1.b1', '45.a1.a1'], 'contains': ['180.i1.b1', '180.l1.a1', '180.n1.a1', '270.c1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1462, -1, 9119, -1, 1581, -1, 9531, -1], 'generators': [288872, 120329, 30, 160673], 'label': '2160.dm.90.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862625
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 216, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '18.e1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '180.i1.b1', '180.m1.a1', '270.d1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1140, -1, 9888, -1, 146, -1, 9825, -1], 'generators': [288872, 30, 160673, 288152], 'label': '2160.dm.90.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 168862626
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.a1', '18.f1.a1', '45.a1.a1'], 'contains': ['180.l1.a1', '180.l1.b1', '180.m1.a1', '270.e1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [697, -1, 9956, -1, 410, -1, 9727, -1], 'generators': [288206, 288872, 160649, 30], 'label': '2160.dm.90.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '90.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862627
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.d1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.d1.a1', '540.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5077, -1, 1592, -1, 5739, -1, 2165, -1], 'generators': [54, 25866086400, 288152], 'label': '2160.dm.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '432.741', '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': '1.1'}
  • id: 168862628
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '36.b1.b1', '36.d1.b1', '54.a1.b1'], 'contains': ['216.a1.a1', '216.b1.b1', '216.d1.b1', '540.a1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5077, -1, 4938, -1, 5739, -1, 5564, -1], 'generators': [54, 25866086400, 160679], 'label': '2160.dm.108.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '108.a1.b1', 'projective_image': '432.741', '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': '1.1'}
  • id: 168862629
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.c1.b1', '36.e1.a1', '54.a1.a1', '54.a1.b1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.e1.a1', '540.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2823, -1, 6287, -1, 3247, -1, 4788, -1], 'generators': [54, 333513, 25866086400], 'label': '2160.dm.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '432.741', '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: 168862630
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.g1.a1', '36.h1.a1', '36.j1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.e1.a1', '540.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8960, -1, 780, -1, 8441, -1, 1446, -1], 'generators': [333567, 25866086400, 328473], 'label': '2160.dm.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '432.741', '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: 168862631
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.b1', '36.g1.b1', '36.h1.b1', '36.j1.b1', '54.a1.b1'], 'contains': ['216.b1.b1', '216.d1.b1', '216.e1.a1', '540.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8960, -1, 5429, -1, 8441, -1, 5228, -1], 'generators': [333567, 25866086400, 45359], 'label': '2160.dm.108.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '108.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862632
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.k1.a1', '54.a1.a1', '54.c1.a1', '54.d1.a1'], 'contains': ['216.b1.a1', '216.c1.a1', '540.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2339, -1, 8051, -1, 2737, -1, 5726, -1], 'generators': [288872, 25866086400, 288152], 'label': '2160.dm.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '432.741', '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: 168862633
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.b1', '36.k1.b1', '54.a1.b1', '54.c1.b1', '54.d1.a1'], 'contains': ['216.b1.b1', '216.c1.a1', '540.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2339, -1, 8595, -1, 2737, -1, 7883, -1], 'generators': [288872, 25866086400, 160625], 'label': '2160.dm.108.d1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862634
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.o1.a1', '30.c1.a1', '54.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1599, -1, 8688, -1, 2622, -1, 8468, -1], 'generators': [54, 120359, 333513, 25866086400, 328472, 338552], 'label': '2160.dm.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862635
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.o1.a1', '54.a1.a1', '54.c1.b1', '54.e1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '540.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2051, -1, 7745, -1, 2910, -1, 5832, -1], 'generators': [288206, 288872, 25866086400], 'label': '2160.dm.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862636
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.b1', '36.o1.b1', '54.a1.b1', '54.c1.a1', '54.e1.a1'], 'contains': ['216.c1.a1', '216.d1.b1', '540.e1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2051, -1, 8496, -1, 2910, -1, 7777, -1], 'generators': [288872, 160649, 25866086400], 'label': '2160.dm.108.e1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.e1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862637
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '36.m1.a1', '54.b1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.c1.a1', '540.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [447, -1, 9533, -1, 1176, -1, 9127, -1], 'generators': [288872, 120305, 25866086400], 'label': '2160.dm.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '432.741', '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: 168862638
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '36.n1.a1', '54.b1.a1', '54.c1.a1', '54.c1.b1'], 'contains': ['216.c1.a1', '540.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1735, -1, 8895, -1, 2016, -1, 8996, -1], 'generators': [288872, 25866086400, 120329], 'label': '2160.dm.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862639
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.b1.a1', '60.a1.a1', '60.a1.b1', '60.b1.a1', '60.d1.a1', '60.n1.a1', '60.n1.b1', '60.o1.a1'], 'contains': ['240.a1.a1', '360.h1.a1', '360.h1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3215, 3848, 8296, 7193, 3382, 4886, 7031, 6901], 'generators': [333513, 328472, 338552], 'label': '2160.dm.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.b1.a1', '60.a1.a1', '60.a1.b1', '60.b1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862640
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.8', 'aut_weyl_index': 216, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.a1', '60.c1.a1', '60.c1.b1', '60.d1.a1'], 'contains': ['240.a1.a1', '360.b1.a1', '360.b1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4805, -1, 3732, -1, 5266, -1, 4399, -1], 'generators': [54, 328472, 338552], 'label': '2160.dm.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 168862641
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.a1.a1', '60.e1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.b1.a1', '360.a1.a1', '360.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4624, -1, 2844, -1, 4901, -1, 3615, -1], 'generators': [54, 30, 328472], 'label': '2160.dm.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862642
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '40.a1.a1', '60.e1.b1', '60.f1.b1', '60.g1.b1'], 'contains': ['240.b1.b1', '360.a1.a1', '360.b1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4624, -1, 4515, -1, 4901, -1, 6348, -1], 'generators': [54, 298233, 30], 'label': '2160.dm.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '120.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862643
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.d1.a1', '60.e1.a1', '60.h1.a1', '60.l1.a1'], 'contains': ['240.b1.a1', '360.c1.a1', '360.d1.a1', '360.e1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6282, -1, 2348, -1, 6642, -1, 2570, -1], 'generators': [30, 5760, 288152], 'label': '2160.dm.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862644
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '40.d1.b1', '60.e1.b1', '60.h1.b1', '60.l1.b1'], 'contains': ['240.b1.b1', '360.c1.b1', '360.d1.b1', '360.e1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6282, -1, 5706, -1, 6642, -1, 7104, -1], 'generators': [298233, 30, 160673], 'label': '2160.dm.120.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862645
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.l1.a1', '12.m1.a1', '18.a1.a1', '18.b1.a1', '30.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4937, -1, 2869, -1, 5094, -1, 2813, -1], 'generators': [54, 333513, 25866086400, 30, 328472, 288152], 'label': '2160.dm.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '6.d1.a1', 'projective_image': '432.741', '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': '36.10'}
  • id: 168862646
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '40.d1.a1', '60.f1.a1', '60.i1.a1', '60.l1.a1'], 'contains': ['240.b1.a1', '360.c1.a1', '360.f1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6102, -1, 2265, -1, 5897, -1, 2821, -1], 'generators': [30, 328472, 288152], 'label': '2160.dm.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862647
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '40.d1.b1', '60.f1.b1', '60.i1.b1', '60.l1.b1'], 'contains': ['240.b1.b1', '360.c1.b1', '360.f1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6102, -1, 5541, -1, 5897, -1, 7192, -1], 'generators': [30, 160673, 338552], 'label': '2160.dm.120.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '120.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862648
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '40.d1.a1', '60.j1.a1'], 'contains': ['240.c1.a1', '360.e1.a1', '360.f1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9165, -1, 499, -1, 8742, -1, 1158, -1], 'generators': [338582, 328472, 288152], 'label': '2160.dm.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '120.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862649
    {'ambient': '2160.dm', 'aut_centralizer_order': 36, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '48.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '40.d1.b1', '60.j1.b1'], 'contains': ['240.c1.b1', '360.e1.b1', '360.f1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9165, -1, 5789, -1, 8742, -1, 6261, -1], 'generators': [288183, 151913, 338552], 'label': '2160.dm.120.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '120.f1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862650
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '40.d1.a1', '60.a1.a1', '60.c1.a1', '60.k1.a1'], 'contains': ['240.a1.a1', '360.d1.a1', '360.f1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6508, -1, 2568, -1, 6883, -1, 2261, -1], 'generators': [328472, 338552, 288152], 'label': '2160.dm.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '120.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862651
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '40.d1.b1', '60.a1.b1', '60.c1.b1', '60.k1.b1'], 'contains': ['240.a1.a1', '360.d1.b1', '360.f1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6508, -1, 5989, -1, 6883, -1, 7506, -1], 'generators': [160625, 328472, 338552], 'label': '2160.dm.120.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '120.g1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862652
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '40.b1.a1', '60.g1.a1', '60.l1.a1', '60.m1.a1'], 'contains': ['240.b1.a1', '360.g1.a1', '360.h1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3664, -1, 3814, -1, 3757, -1, 5981, -1], 'generators': [333513, 30, 328472], 'label': '2160.dm.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.h1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862653
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '40.b1.a1', '60.g1.b1', '60.l1.b1', '60.m1.b1'], 'contains': ['240.b1.b1', '360.g1.a1', '360.h1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3664, -1, 7515, -1, 3757, -1, 7681, -1], 'generators': [333513, 298233, 30], 'label': '2160.dm.120.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.h1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862654
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '40.e1.a1', '60.e1.a1', '60.i1.a1', '60.m1.a1'], 'contains': ['240.b1.a1', '360.i1.a1', '360.j1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5610, -1, 2038, -1, 6211, -1, 2908, -1], 'generators': [288206, 30, 5760], 'label': '2160.dm.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.i1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862655
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '40.e1.b1', '60.e1.b1', '60.i1.b1', '60.m1.b1'], 'contains': ['240.b1.b1', '360.i1.b1', '360.j1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5610, -1, 6347, -1, 6211, -1, 6864, -1], 'generators': [160649, 298233, 30], 'label': '2160.dm.120.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.i1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862656
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['12.e1.b1', '12.f1.b1', '12.g1.b1', '12.h1.b1', '12.i1.b1', '12.l1.b1', '12.m1.b1', '18.a1.b1', '18.b1.b1', '30.d1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4937, -1, 6521, -1, 5094, -1, 6486, -1], 'generators': [54, 160649, 25866086400, 298233, 30, 5041], 'label': '2160.dm.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '6.d1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862657
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '40.e1.a1', '60.j1.a1'], 'contains': ['240.c1.a1', '360.i1.a1', '360.l1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8946, -1, 416, -1, 8885, -1, 1245, -1], 'generators': [288206, 328502, 5760], 'label': '2160.dm.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '120.j1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862658
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '40.e1.b1', '60.j1.b1'], 'contains': ['240.c1.b1', '360.i1.b1', '360.l1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8946, -1, 6095, -1, 8885, -1, 6127, -1], 'generators': [160649, 288183, 298233], 'label': '2160.dm.120.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '120.j1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862659
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '40.e1.a1', '60.c1.a1', '60.k1.a1', '60.n1.a1'], 'contains': ['240.a1.a1', '360.i1.a1', '360.k1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5963, -1, 2452, -1, 7114, -1, 2348, -1], 'generators': [288206, 328472, 338552], 'label': '2160.dm.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862660
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '40.e1.b1', '60.c1.b1', '60.k1.b1', '60.n1.b1'], 'contains': ['240.a1.a1', '360.i1.b1', '360.k1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5963, -1, 6959, -1, 7114, -1, 7326, -1], 'generators': [160649, 328472, 338552], 'label': '2160.dm.120.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '120.k1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862661
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '40.e1.a1', '60.f1.a1', '60.h1.a1', '60.m1.a1'], 'contains': ['240.b1.a1', '360.j1.a1', '360.k1.a1', '360.l1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5727, -1, 1785, -1, 6763, -1, 2643, -1], 'generators': [288206, 30, 328472], 'label': '2160.dm.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '120.l1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862662
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '40.e1.b1', '60.f1.b1', '60.h1.b1', '60.m1.b1'], 'contains': ['240.b1.b1', '360.j1.b1', '360.k1.b1', '360.l1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5727, -1, 6416, -1, 6763, -1, 6792, -1], 'generators': [160649, 30, 338552], 'label': '2160.dm.120.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '120.l1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862663
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '40.c1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1'], 'contains': ['240.b1.a1', '360.m1.a1', '360.n1.a1', '360.o1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6834, -1, 2130, -1, 7961, -1, 3182, -1], 'generators': [333567, 30, 328472], 'label': '2160.dm.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.m1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862664
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '40.c1.a1', '60.g1.b1', '60.h1.b1', '60.i1.b1'], 'contains': ['240.b1.b1', '360.m1.a1', '360.n1.b1', '360.o1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6834, -1, 6163, -1, 7961, -1, 6054, -1], 'generators': [333567, 298233, 30], 'label': '2160.dm.120.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.m1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862665
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '40.c1.a1', '60.j1.a1'], 'contains': ['240.c1.a1', '360.n1.a1', '360.o1.a1', '360.o1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9283, -1, 617, -1, 9493, -1, 1949, -1], 'generators': [333567, 338582, 328472], 'label': '2160.dm.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '120.n1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862666
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '40.c1.a1', '60.j1.b1'], 'contains': ['240.c1.b1', '360.n1.b1', '360.o1.a1', '360.o1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9283, -1, 4140, -1, 9493, -1, 4126, -1], 'generators': [333567, 288183, 298233], 'label': '2160.dm.120.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '120.n1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862667
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.n1.b1', '12.o1.a1', '30.e1.a1', '54.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2404, -1, 8131, -1, 3264, -1, 7476, -1], 'generators': [333513, 160649, 25866086400, 328472, 338552, 288152], 'label': '2160.dm.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862668
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '40.c1.a1', '60.d1.a1', '60.k1.a1', '60.k1.b1'], 'contains': ['240.a1.a1', '360.n1.a1', '360.n1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7059, -1, 4008, -1, 8228, -1, 4238, -1], 'generators': [333567, 328472, 338552], 'label': '2160.dm.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862669
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '135.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '27.a1.a1', '45.a1.a1'], 'contains': ['270.a1.a1', '270.a1.b1', '270.b1.a1', '270.c1.a1', '270.c1.b1', '270.d1.a1', '270.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1100, -1, 9248, -1, 705, -1, 9654, -1], 'generators': [54, 288872, 160679, 288152], 'label': '2160.dm.135.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '135.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862670
    {'ambient': '2160.dm', 'aut_centralizer_order': 432, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '2.d1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.b1.b1', '72.a1.a1', '72.c1.a1', '72.c1.b1', '72.g1.a1', '72.j1.a1', '72.j1.b1', '72.m1.a1'], 'contains': ['432.a1.a1', '720.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8237, 9062, 3136, 282, 6340, 1828, 3973, 1870], 'generators': [25866086400, 30], 'label': '2160.dm.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['16.a1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1', '720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.40', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862671
    {'ambient': '2160.dm', 'aut_centralizer_order': 108, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.b1.a1', '72.d1.a1', '72.f1.a1', '72.h1.a1', '72.i1.a1', '72.k1.a1', '72.n1.a1'], 'contains': ['432.a1.a1', '720.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7755, -1, 1313, -1, 7406, -1, 2399, -1], 'generators': [25866086400, 328472], 'label': '2160.dm.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862672
    {'ambient': '2160.dm', 'aut_centralizer_order': 108, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '4.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.b1', '48.c1.b1', '72.b1.b1', '72.d1.b1', '72.f1.b1', '72.h1.b1', '72.i1.b1', '72.k1.b1', '72.n1.b1'], 'contains': ['432.a1.a1', '720.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7755, -1, 4878, -1, 7406, -1, 5105, -1], 'generators': [25866086400, 298233], 'label': '2160.dm.144.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '144.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862673
    {'ambient': '2160.dm', 'aut_centralizer_order': 54, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.c1.a1', '48.c1.b1', '72.e1.a1', '72.l1.a1', '72.o1.a1'], 'contains': ['432.a1.a1', '720.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9587, -1, 286, -1, 9004, -1, 1937, -1], 'generators': [25866086400, 328502], 'label': '2160.dm.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862674
    {'ambient': '2160.dm', 'aut_centralizer_order': 54, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 432, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '48.c1.a1', '48.c1.b1', '72.e1.b1', '72.l1.b1', '72.o1.b1'], 'contains': ['432.a1.a1', '720.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9587, -1, 3583, -1, 9004, -1, 3859, -1], 'generators': [25866086400, 338582], 'label': '2160.dm.144.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '144.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862675
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.c1.a1', '60.e1.a1', '90.a1.a1'], 'contains': ['360.b1.a1', '360.d1.a1', '360.i1.a1', '540.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5061, -1, 2688, -1, 5410, -1, 2482, -1], 'generators': [54, 5760, 288152], 'label': '2160.dm.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862676
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '60.c1.b1', '60.e1.b1', '90.a1.b1'], 'contains': ['360.b1.b1', '360.d1.b1', '360.i1.b1', '540.a1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5061, -1, 5067, -1, 5410, -1, 7594, -1], 'generators': [54, 298233, 160679], 'label': '2160.dm.180.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '180.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862677
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.c1.a1', '60.f1.a1', '90.a1.a1'], 'contains': ['360.b1.a1', '360.f1.a1', '360.k1.a1', '540.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5278, -1, 2624, -1, 5520, -1, 2415, -1], 'generators': [54, 328472, 288152], 'label': '2160.dm.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '180.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862678
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.n1.a1', '12.o1.a1', '30.e1.b1', '54.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2404, -1, 8453, -1, 3264, -1, 7843, -1], 'generators': [333513, 25866086400, 160625, 120329, 328472, 338552], 'label': '2160.dm.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862679
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.b1', '60.c1.b1', '60.f1.b1', '90.a1.b1'], 'contains': ['360.b1.b1', '360.f1.b1', '360.k1.b1', '540.a1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5278, -1, 5476, -1, 5520, -1, 7439, -1], 'generators': [54, 160679, 338552], 'label': '2160.dm.180.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '180.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862680
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.d1.a1', '60.g1.a1', '90.a1.a1'], 'contains': ['360.b1.a1', '360.h1.a1', '360.n1.a1', '540.b1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3574, -1, 3423, -1, 4574, -1, 4073, -1], 'generators': [54, 333513, 328472], 'label': '2160.dm.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862681
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '60.d1.a1', '60.g1.b1', '90.a1.b1'], 'contains': ['360.b1.b1', '360.h1.b1', '360.n1.b1', '540.b1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3574, -1, 7071, -1, 4574, -1, 6739, -1], 'generators': [54, 333513, 298233], 'label': '2160.dm.180.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '180.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862682
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.e1.a1', '60.f1.a1', '90.b1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '360.j1.a1', '540.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5191, -1, 2798, -1, 5011, -1, 3548, -1], 'generators': [54, 30, 288152], 'label': '2160.dm.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '180.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862683
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '60.e1.b1', '60.f1.b1', '90.b1.b1'], 'contains': ['360.a1.a1', '360.c1.b1', '360.j1.b1', '540.a1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5191, -1, 4588, -1, 5011, -1, 7259, -1], 'generators': [54, 160649, 30], 'label': '2160.dm.180.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '180.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862684
    {'ambient': '2160.dm', 'aut_centralizer_order': 64, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '60.g1.a1', '60.g1.b1', '90.b1.a1', '90.b1.b1', '90.c1.a1'], 'contains': ['360.a1.a1', '360.g1.a1', '360.m1.a1', '540.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2772, -1, 6641, -1, 3035, -1, 6692, -1], 'generators': [54, 333513, 30], 'label': '2160.dm.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862685
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.h1.a1', '60.i1.a1', '90.b1.a1'], 'contains': ['360.c1.a1', '360.j1.a1', '360.m1.a1', '540.c1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6663, -1, 1841, -1, 6101, -1, 3234, -1], 'generators': [333567, 328473, 30], 'label': '2160.dm.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '180.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862686
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.b1', '60.h1.b1', '60.i1.b1', '90.b1.b1'], 'contains': ['360.c1.b1', '360.j1.b1', '360.m1.a1', '540.c1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6663, -1, 6919, -1, 6101, -1, 6932, -1], 'generators': [333567, 45329, 30], 'label': '2160.dm.180.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.b1', 'old_label': '180.f1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862687
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.h1.a1', '60.k1.a1', '90.a1.a1'], 'contains': ['360.d1.a1', '360.k1.a1', '360.n1.a1', '540.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6867, -1, 1735, -1, 8142, -1, 2002, -1], 'generators': [333567, 328473, 5760], 'label': '2160.dm.180.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '180.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862688
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.b1', '60.h1.b1', '60.k1.b1', '90.a1.b1'], 'contains': ['360.d1.b1', '360.k1.b1', '360.n1.b1', '540.c1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6867, -1, 7126, -1, 8142, -1, 7393, -1], 'generators': [333567, 160679, 338552], 'label': '2160.dm.180.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '180.g1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862689
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['1080.b1.a1', '1080.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1', '4.f1.b1', '4.g1.b1', '6.b1.b1', '6.d1.b1', '10.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4195, 5415, 7284, 6223, 4675, 3355, 6709, 3482], 'generators': [54, 333513, 160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1', '10.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862690
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.n1.a1', '12.n1.b1', '30.f1.a1', '54.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [763, -1, 9341, -1, 1692, -1, 7672, -1], 'generators': [288206, 333513, 25866086400, 160679, 328472, 338552], 'label': '2160.dm.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862691
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.h1.a1', '60.j1.a1'], 'contains': ['360.e1.a1', '360.l1.a1', '360.o1.a1', '540.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9345, -1, 534, -1, 9406, -1, 1091, -1], 'generators': [333567, 328473, 5790], 'label': '2160.dm.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '180.h1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862692
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.b1', '60.h1.b1', '60.j1.b1'], 'contains': ['360.e1.b1', '360.l1.b1', '360.o1.b1', '540.c1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9345, -1, 5972, -1, 9406, -1, 6194, -1], 'generators': [333567, 160649, 293943], 'label': '2160.dm.180.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.b1', 'old_label': '180.h1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862693
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '60.l1.a1', '90.b1.a1', '90.d1.a1', '90.e1.a1'], 'contains': ['360.c1.a1', '360.g1.a1', '540.d1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2508, -1, 7812, -1, 2408, -1, 6579, -1], 'generators': [288872, 30, 288152], 'label': '2160.dm.180.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.i1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862694
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.b1', '60.l1.b1', '90.b1.b1', '90.d1.b1', '90.e1.a1'], 'contains': ['360.c1.b1', '360.g1.a1', '540.d1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2508, -1, 8576, -1, 2408, -1, 8303, -1], 'generators': [288872, 30, 160673], 'label': '2160.dm.180.i1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.i1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862695
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '60.i1.a1', '60.j1.a1', '60.k1.a1', '90.a1.a1'], 'contains': ['360.f1.a1', '360.i1.a1', '360.n1.a1', '540.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7223, -1, 2028, -1, 8315, -1, 1666, -1], 'generators': [333567, 328472, 288152], 'label': '2160.dm.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '180.j1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862696
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.b1', '60.i1.b1', '60.j1.b1', '60.k1.b1', '90.a1.b1'], 'contains': ['360.f1.b1', '360.i1.b1', '360.n1.b1', '540.c1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7223, -1, 6686, -1, 8315, -1, 6978, -1], 'generators': [333567, 298233, 151919], 'label': '2160.dm.180.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '180.j1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862697
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '60.a1.a1', '60.l1.a1', '90.a1.a1'], 'contains': ['360.d1.a1', '360.f1.a1', '360.h1.a1', '540.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4128, -1, 3333, -1, 3955, -1, 3281, -1], 'generators': [333513, 328472, 288152], 'label': '2160.dm.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '180.k1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862698
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.b1', '60.a1.b1', '60.l1.b1', '90.a1.b1'], 'contains': ['360.d1.b1', '360.f1.b1', '360.h1.b1', '540.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4128, -1, 7571, -1, 3955, -1, 8058, -1], 'generators': [298233, 160625, 5041], 'label': '2160.dm.180.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '180.k1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862699
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '60.m1.a1', '90.b1.a1', '90.d1.b1', '90.f1.a1'], 'contains': ['360.g1.a1', '360.j1.a1', '540.e1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2064, -1, 7621, -1, 2518, -1, 6646, -1], 'generators': [288206, 288872, 30], 'label': '2160.dm.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.l1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862700
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.b1', '60.m1.b1', '90.b1.b1', '90.d1.a1', '90.f1.a1'], 'contains': ['360.g1.a1', '360.j1.b1', '540.e1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2064, -1, 8513, -1, 2518, -1, 8188, -1], 'generators': [288872, 160649, 30], 'label': '2160.dm.180.l1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.l1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862701
    {'ambient': '2160.dm', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.12219', 'aut_weyl_index': 9, 'centralizer': '48.a1.a1', 'complements': ['270.c1.b1', '270.d1.a1', '270.c1.a1', '270.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5633, 9240, 3486, 479, 5753, 542, 3830, 861], 'generators': [54, 25866086400, 30, 328472, 338552], 'label': '2160.dm.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '40.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 168862702
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '36.m1.a1', '90.c1.a1', '90.e1.a1', '90.f1.a1'], 'contains': ['360.g1.a1', '540.f1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [764, -1, 9835, -1, 504, -1, 9727, -1], 'generators': [288872, 120353, 30], 'label': '2160.dm.180.m1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.m1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862703
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.a1', '36.n1.a1', '90.c1.a1', '90.d1.a1', '90.d1.b1'], 'contains': ['360.g1.a1', '540.g1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1513, -1, 8948, -1, 1650, -1, 9303, -1], 'generators': [288872, 120329, 30], 'label': '2160.dm.180.n1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.n1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862704
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '60.m1.a1', '60.n1.a1', '90.a1.a1'], 'contains': ['360.h1.a1', '360.i1.a1', '360.k1.a1', '540.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3776, -1, 4037, -1, 4031, -1, 3327, -1], 'generators': [288206, 333513, 328472], 'label': '2160.dm.180.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '180.o1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862705
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.b1', '60.m1.b1', '60.n1.b1', '90.a1.b1'], 'contains': ['360.h1.b1', '360.i1.b1', '360.k1.b1', '540.e1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3776, -1, 7382, -1, 4031, -1, 7959, -1], 'generators': [160649, 298233, 5041], 'label': '2160.dm.180.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '180.o1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862706
    {'ambient': '2160.dm', 'aut_centralizer_order': 288, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.b1.b1', '108.a1.a1', '108.a1.b1', '108.b1.a1'], 'contains': ['432.a1.a1', '1080.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4486, -1, 3599, -1, 5600, -1, 3916, -1], 'generators': [54, 25866086400], 'label': '2160.dm.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862707
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '108.a1.a1', '108.c1.a1', '108.d1.a1'], 'contains': ['432.a1.a1', '1080.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7847, -1, 1025, -1, 7257, -1, 2124, -1], 'generators': [25866086400, 288152], 'label': '2160.dm.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862708
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.d1.b1', '72.e1.b1', '72.f1.b1', '108.a1.b1', '108.c1.b1', '108.d1.b1'], 'contains': ['432.a1.a1', '1080.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7847, -1, 5258, -1, 7257, -1, 5469, -1], 'generators': [25866086400, 160625], 'label': '2160.dm.216.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '216.b1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862709
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.h1.a1', '72.h1.b1', '108.b1.a1', '108.d1.a1', '108.d1.b1', '108.e1.a1', '108.e1.b1', '108.f1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '1080.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2273, -1, 7982, -1, 2912, -1, 6417, -1], 'generators': [333513, 25866086400], 'label': '2160.dm.216.c1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862710
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '108.a1.a1', '108.c1.a1', '108.e1.a1'], 'contains': ['432.a1.a1', '1080.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8147, -1, 912, -1, 7499, -1, 2181, -1], 'generators': [288206, 25866086400], 'label': '2160.dm.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862711
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.b1', '72.j1.b1', '72.k1.b1', '72.l1.b1', '108.a1.b1', '108.c1.b1', '108.e1.b1'], 'contains': ['432.a1.a1', '1080.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8147, -1, 5204, -1, 7499, -1, 5269, -1], 'generators': [160649, 25866086400], 'label': '2160.dm.216.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '216.d1.b1', 'projective_image': '432.741', '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': '1.1'}
  • id: 168862712
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1152.93925', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.h1.a1', '24.h1.b1', '40.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3037, 6004, 7631, 6074, 3559, 3953, 6241, 4033], 'generators': [333513, 25866086400, 30, 328472, 338552], 'label': '2160.dm.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862713
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1', '72.n1.b1', '72.o1.a1', '72.o1.b1', '108.b1.a1', '108.c1.a1', '108.c1.b1'], 'contains': ['432.a1.a1', '1080.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8737, -1, 3042, -1, 8136, -1, 2812, -1], 'generators': [333567, 25866086400], 'label': '2160.dm.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862714
    {'ambient': '2160.dm', 'aut_centralizer_order': 216, 'aut_label': '240.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 216, 'centralizer': '8.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.g1.a1', '120.g1.b1', '120.k1.a1', '120.k1.b1', '120.o1.a1'], 'contains': ['720.b1.a1', '720.b1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6269, 7271, 3927, 2060, 6883, 2770, 4266, 2610], 'generators': [328472, 338552], 'label': '2160.dm.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1'], 'normal_contains': ['2160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '8.3', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 168862715
    {'ambient': '2160.dm', 'aut_centralizer_order': 216, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.a1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.h1.a1', '120.i1.a1', '120.l1.a1', '120.m1.a1'], 'contains': ['720.a1.a1', '720.b1.a1', '720.c1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5934, -1, 2340, -1, 6680, -1, 2919, -1], 'generators': [30, 328472], 'label': '2160.dm.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862716
    {'ambient': '2160.dm', 'aut_centralizer_order': 216, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '80.a1.a1', '120.c1.b1', '120.d1.b1', '120.e1.b1', '120.h1.b1', '120.i1.b1', '120.l1.b1', '120.m1.b1'], 'contains': ['720.a1.a1', '720.b1.b1', '720.c1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5934, -1, 5557, -1, 6680, -1, 6631, -1], 'generators': [298233, 30], 'label': '2160.dm.240.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '240.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862717
    {'ambient': '2160.dm', 'aut_centralizer_order': 108, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.a1.a1', '120.f1.a1', '120.j1.a1', '120.n1.a1'], 'contains': ['720.b1.a1', '720.c1.a1', '720.c1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9013, -1, 590, -1, 8813, -1, 2039, -1], 'generators': [338582, 328472], 'label': '2160.dm.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '240.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862718
    {'ambient': '2160.dm', 'aut_centralizer_order': 108, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '80.a1.a1', '120.f1.b1', '120.j1.b1', '120.n1.b1'], 'contains': ['720.b1.b1', '720.c1.a1', '720.c1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9013, -1, 4470, -1, 8813, -1, 4167, -1], 'generators': [288183, 298233], 'label': '2160.dm.240.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '240.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862719
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '90.a1.a1', '90.b1.a1', '135.a1.a1'], 'contains': ['540.a1.a1', '540.b1.a1', '540.c1.a1', '540.d1.a1', '540.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3289, -1, 6328, -1, 3117, -1, 5911, -1], 'generators': [54, 288872, 288152], 'label': '2160.dm.270.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862720
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.b1', '90.a1.b1', '90.b1.b1', '135.a1.a1'], 'contains': ['540.a1.b1', '540.b1.a1', '540.c1.b1', '540.d1.b1', '540.e1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3289, -1, 7697, -1, 3117, -1, 8008, -1], 'generators': [54, 288872, 160679], 'label': '2160.dm.270.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862721
    {'ambient': '2160.dm', 'aut_centralizer_order': 64, 'aut_label': '270.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '54.b1.a1', '90.c1.a1', '135.a1.a1'], 'contains': ['540.b1.a1', '540.f1.a1', '540.g1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1093, -1, 9356, -1, 864, -1, 9516, -1], 'generators': [54, 288872, 120359], 'label': '2160.dm.270.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862722
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '270.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '54.c1.a1', '90.d1.a1', '135.a1.a1'], 'contains': ['540.d1.a1', '540.e1.b1', '540.g1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1631, -1, 8803, -1, 1931, -1, 9226, -1], 'generators': [288872, 160649, 288152], 'label': '2160.dm.270.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862723
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': ['270.c1.b1', '270.d1.a1', '270.c1.a1', '270.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.a1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1', '24.n1.b1', '24.o1.a1', '40.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7461, 8157, 3615, 1409, 8501, 1545, 3492, 1648], 'generators': [333567, 25866086400, 30, 328472, 338552], 'label': '2160.dm.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.741', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862724
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '270.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '54.c1.b1', '90.d1.b1', '135.a1.a1'], 'contains': ['540.d1.b1', '540.e1.a1', '540.g1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1631, -1, 9033, -1, 1931, -1, 9402, -1], 'generators': [288872, 160625, 120329], 'label': '2160.dm.270.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862725
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '270.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '54.d1.a1', '90.e1.a1', '135.a1.a1'], 'contains': ['540.d1.a1', '540.d1.b1', '540.f1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1225, -1, 9264, -1, 1015, -1, 9449, -1], 'generators': [288872, 160625, 288152], 'label': '2160.dm.270.d1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '270.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862726
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '270.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '54.e1.a1', '90.f1.a1', '135.a1.a1'], 'contains': ['540.e1.a1', '540.e1.b1', '540.f1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [968, -1, 9504, -1, 1091, -1, 9356, -1], 'generators': [288206, 288872, 160679], 'label': '2160.dm.270.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '270.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862727
    {'ambient': '2160.dm', 'aut_centralizer_order': 576, 'aut_label': '360.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.a1.a1', 'complements': ['6.e1.b1', '6.a1.a1', '6.e1.a1', '6.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.c1.a1', '120.c1.b1', '180.d1.a1', '180.d1.b1', '180.e1.a1'], 'contains': ['720.a1.a1', '1080.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4396, 9128, 3095, 1003, 5066, 1230, 4216, 1401], 'generators': [54, 30], 'label': '2160.dm.360.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': ['40.a1.a1', '72.a1.a1'], 'normal_contains': ['720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '180.28', 'quotient_action_kernel_order': 180, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862728
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.b1.a1', '120.c1.a1', '180.a1.a1', '180.b1.a1', '180.c1.a1'], 'contains': ['720.b1.a1', '1080.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4793, -1, 2855, -1, 5413, -1, 3061, -1], 'generators': [54, 328472], 'label': '2160.dm.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862729
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.b1', '120.b1.a1', '120.c1.b1', '180.a1.b1', '180.b1.b1', '180.c1.b1'], 'contains': ['720.b1.b1', '1080.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4793, -1, 4706, -1, 5413, -1, 6357, -1], 'generators': [54, 298233], 'label': '2160.dm.360.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '360.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862730
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.d1.a1', '120.e1.a1', '180.d1.a1', '180.f1.a1', '180.i1.a1'], 'contains': ['720.a1.a1', '1080.b1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6086, -1, 2603, -1, 6058, -1, 3119, -1], 'generators': [30, 288152], 'label': '2160.dm.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '360.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862731
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '120.d1.b1', '120.e1.b1', '180.d1.b1', '180.f1.b1', '180.i1.b1'], 'contains': ['720.a1.a1', '1080.b1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6086, -1, 5341, -1, 6058, -1, 6964, -1], 'generators': [30, 160673], 'label': '2160.dm.360.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '360.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862732
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.d1.a1', '120.g1.a1', '180.a1.a1', '180.g1.a1', '180.k1.a1'], 'contains': ['720.b1.a1', '1080.b1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6476, -1, 2672, -1, 6801, -1, 2497, -1], 'generators': [5760, 288152], 'label': '2160.dm.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '360.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862733
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '120.d1.b1', '120.g1.b1', '180.a1.b1', '180.g1.b1', '180.k1.b1'], 'contains': ['720.b1.b1', '1080.b1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6476, -1, 6003, -1, 6801, -1, 7156, -1], 'generators': [298233, 160625], 'label': '2160.dm.360.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '360.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862734
    {'ambient': '2160.dm', 'aut_centralizer_order': 9, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 36, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '40.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8195, -1, 1704, -1, 7263, -1, 1604, -1], 'generators': [25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862735
    {'ambient': '2160.dm', 'aut_centralizer_order': 72, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.d1.a1', '120.f1.a1', '180.h1.a1'], 'contains': ['720.c1.a1', '1080.b1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9475, -1, 511, -1, 8732, -1, 1499, -1], 'generators': [5790, 288152], 'label': '2160.dm.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '360.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862737
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1', '180.b1.a1', '180.j1.a1', '180.k1.a1'], 'contains': ['720.b1.a1', '1080.b1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6889, -1, 2420, -1, 7041, -1, 2301, -1], 'generators': [328472, 288152], 'label': '2160.dm.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '360.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862738
    {'ambient': '2160.dm', 'aut_centralizer_order': 144, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '120.e1.b1', '120.f1.b1', '120.g1.b1', '180.b1.b1', '180.j1.b1', '180.k1.b1'], 'contains': ['720.b1.b1', '1080.b1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6889, -1, 5787, -1, 7041, -1, 7057, -1], 'generators': [160625, 338552], 'label': '2160.dm.360.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '360.f1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862739
    {'ambient': '2160.dm', 'aut_centralizer_order': 192, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.h1.a1', '120.h1.b1', '180.e1.a1', '180.i1.a1', '180.i1.b1', '180.l1.a1', '180.l1.b1', '180.m1.a1', '180.n1.a1'], 'contains': ['720.a1.a1', '1080.c1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2221, -1, 8360, -1, 2603, -1, 7249, -1], 'generators': [333513, 30], 'label': '2160.dm.360.g1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862740
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.a1.a1', '120.h1.a1', '180.c1.a1', '180.k1.a1', '180.o1.a1'], 'contains': ['720.b1.a1', '1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3774, -1, 3812, -1, 3993, -1, 4117, -1], 'generators': [333513, 328472], 'label': '2160.dm.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '360.h1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862741
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.b1', '120.a1.a1', '120.h1.b1', '180.c1.b1', '180.k1.b1', '180.o1.b1'], 'contains': ['720.b1.b1', '1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3774, -1, 7487, -1, 3993, -1, 7202, -1], 'generators': [333513, 298233], 'label': '2160.dm.360.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '360.h1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862742
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.i1.a1', '120.j1.a1', '120.k1.a1', '180.a1.a1', '180.j1.a1', '180.o1.a1'], 'contains': ['720.b1.a1', '1080.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5848, -1, 1738, -1, 7117, -1, 2348, -1], 'generators': [288206, 5760], 'label': '2160.dm.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '360.i1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862743
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.b1', '120.i1.b1', '120.j1.b1', '120.k1.b1', '180.a1.b1', '180.j1.b1', '180.o1.b1'], 'contains': ['720.b1.b1', '1080.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5848, -1, 6269, -1, 7117, -1, 6864, -1], 'generators': [160649, 298233], 'label': '2160.dm.360.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '360.i1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862744
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.i1.a1', '120.l1.a1', '180.d1.a1', '180.f1.a1', '180.l1.a1'], 'contains': ['720.a1.a1', '1080.d1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5450, -1, 1974, -1, 6226, -1, 3211, -1], 'generators': [288206, 30], 'label': '2160.dm.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '360.j1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862745
    {'ambient': '2160.dm', 'aut_centralizer_order': 9, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 36, 'centralizer': '48.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.a1.a1', '24.d1.b1', '24.e1.b1', '24.f1.b1', '24.g1.b1', '40.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8195, -1, 4991, -1, 7263, -1, 5419, -1], 'generators': [25866086400, 30, 328472, 160673, 338552], 'label': '2160.dm.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.d1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862746
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.b1', '120.i1.b1', '120.l1.b1', '180.d1.b1', '180.f1.b1', '180.l1.b1'], 'contains': ['720.a1.a1', '1080.d1.b1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5450, -1, 6543, -1, 6226, -1, 6818, -1], 'generators': [160649, 30], 'label': '2160.dm.360.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '360.j1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862747
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.k1.a1', '120.l1.a1', '180.b1.a1', '180.g1.a1', '180.o1.a1'], 'contains': ['720.b1.a1', '1080.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5675, -1, 1841, -1, 6965, -1, 2544, -1], 'generators': [288206, 328472], 'label': '2160.dm.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.k1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862748
    {'ambient': '2160.dm', 'aut_centralizer_order': 48, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.b1', '120.k1.b1', '120.l1.b1', '180.b1.b1', '180.g1.b1', '180.o1.b1'], 'contains': ['720.b1.b1', '1080.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5675, -1, 6687, -1, 6965, -1, 7010, -1], 'generators': [160649, 338552], 'label': '2160.dm.360.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '360.k1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862749
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '120.j1.a1', '120.l1.a1', '180.h1.a1'], 'contains': ['720.c1.a1', '1080.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8943, -1, 453, -1, 8895, -1, 1565, -1], 'generators': [288206, 328502], 'label': '2160.dm.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '360.l1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862750
    {'ambient': '2160.dm', 'aut_centralizer_order': 24, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.b1', '120.j1.b1', '120.l1.b1', '180.h1.b1'], 'contains': ['720.c1.b1', '1080.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8943, -1, 5930, -1, 8895, -1, 6137, -1], 'generators': [160649, 338582], 'label': '2160.dm.360.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '360.l1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862751
    {'ambient': '2160.dm', 'aut_centralizer_order': 64, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '120.m1.a1', '120.m1.b1', '180.e1.a1', '180.f1.a1', '180.f1.b1'], 'contains': ['720.a1.a1', '1080.e1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6653, -1, 5233, -1, 6462, -1, 4071, -1], 'generators': [333567, 30], 'label': '2160.dm.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.m1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862752
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '120.m1.a1', '120.n1.a1', '120.o1.a1', '180.c1.a1', '180.g1.a1', '180.j1.a1'], 'contains': ['720.b1.a1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7243, -1, 2060, -1, 8052, -1, 2590, -1], 'generators': [333567, 328472], 'label': '2160.dm.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '360.n1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862753
    {'ambient': '2160.dm', 'aut_centralizer_order': 16, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.b1', '120.m1.b1', '120.n1.b1', '120.o1.a1', '180.c1.b1', '180.g1.b1', '180.j1.b1'], 'contains': ['720.b1.b1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7243, -1, 6093, -1, 8052, -1, 5218, -1], 'generators': [333567, 298233], 'label': '2160.dm.360.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '360.n1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862754
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.a1', '120.m1.a1', '120.n1.a1', '120.n1.b1', '180.h1.a1'], 'contains': ['720.c1.a1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9190, -1, 728, -1, 9247, -1, 2451, -1], 'generators': [333567, 328502], 'label': '2160.dm.360.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '360.o1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862755
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.b1', '120.m1.b1', '120.n1.a1', '120.n1.b1', '180.h1.b1'], 'contains': ['720.c1.b1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9190, -1, 4424, -1, 9247, -1, 4024, -1], 'generators': [333567, 338582], 'label': '2160.dm.360.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.b1', 'old_label': '360.o1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862756
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.950', 'aut_weyl_index': 12, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '40.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7659, -1, 1953, -1, 7491, -1, 1742, -1], 'generators': [288206, 25866086400, 30, 328472, 338552], 'label': '2160.dm.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862757
    {'ambient': '2160.dm', 'aut_centralizer_order': 864, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.b1.b1', '144.c1.a1', '144.c1.b1', '216.a1.a1', '216.b1.a1', '216.b1.b1', '216.c1.a1', '216.d1.a1', '216.d1.b1', '216.e1.a1'], 'contains': ['2160.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8108, 7714, 3161, 976, 7257, 2375, 3916, 2299], 'generators': [25866086400], 'label': '2160.dm.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['48.a1.a1', '144.a1.a1'], 'normal_contains': ['2160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.741', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862758
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.a1.a1', '180.b1.a1', '180.d1.a1', '270.a1.a1'], 'contains': ['1080.a1.a1', '1080.b1.a1', '1080.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5061, -1, 2786, -1, 5498, -1, 2867, -1], 'generators': [54, 288152], 'label': '2160.dm.540.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '540.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862759
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.b1', '180.a1.b1', '180.b1.b1', '180.d1.b1', '270.a1.b1'], 'contains': ['1080.a1.a1', '1080.b1.b1', '1080.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5061, -1, 5108, -1, 5498, -1, 7106, -1], 'generators': [54, 160679], 'label': '2160.dm.540.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '540.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862760
    {'ambient': '2160.dm', 'aut_centralizer_order': 128, 'aut_label': '540.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.c1.a1', '180.c1.b1', '180.e1.a1', '270.a1.a1', '270.a1.b1', '270.b1.a1'], 'contains': ['1080.a1.a1', '1080.c1.a1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3407, -1, 6577, -1, 3181, -1, 6578, -1], 'generators': [54, 333513], 'label': '2160.dm.540.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '540.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862761
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.f1.a1', '180.g1.a1', '180.h1.a1', '180.j1.a1', '270.a1.a1'], 'contains': ['1080.b1.a1', '1080.d1.a1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7461, -1, 1508, -1, 7735, -1, 2252, -1], 'generators': [333567, 328473], 'label': '2160.dm.540.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '540.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862762
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.b1', '180.f1.b1', '180.g1.b1', '180.h1.b1', '180.j1.b1', '270.a1.b1'], 'contains': ['1080.b1.b1', '1080.d1.b1', '1080.e1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7461, -1, 6627, -1, 7735, -1, 6914, -1], 'generators': [333567, 45359], 'label': '2160.dm.540.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '540.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862763
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.i1.a1', '180.k1.a1', '270.a1.a1', '270.c1.a1', '270.d1.a1'], 'contains': ['1080.b1.a1', '1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2646, -1, 7882, -1, 2735, -1, 6472, -1], 'generators': [288872, 288152], 'label': '2160.dm.540.d1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '540.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862764
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.b1', '180.i1.b1', '180.k1.b1', '270.a1.b1', '270.c1.b1', '270.d1.a1'], 'contains': ['1080.b1.b1', '1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2646, -1, 8611, -1, 2735, -1, 8046, -1], 'generators': [288872, 160625], 'label': '2160.dm.540.d1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '540.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862765
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.l1.a1', '180.o1.a1', '270.a1.a1', '270.c1.b1', '270.e1.a1'], 'contains': ['1080.c1.a1', '1080.d1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2095, -1, 7603, -1, 2822, -1, 6525, -1], 'generators': [288206, 288872], 'label': '2160.dm.540.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '540.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862766
    {'ambient': '2160.dm', 'aut_centralizer_order': 32, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.b1', '180.l1.b1', '180.o1.b1', '270.a1.b1', '270.c1.a1', '270.e1.a1'], 'contains': ['1080.c1.a1', '1080.d1.b1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2095, -1, 8512, -1, 2822, -1, 7970, -1], 'generators': [288872, 160649], 'label': '2160.dm.540.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '540.e1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862767
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.950', 'aut_weyl_index': 12, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.a1.a1', '24.i1.b1', '24.j1.b1', '24.k1.b1', '24.l1.b1', '40.e1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7659, -1, 4660, -1, 7491, -1, 5055, -1], 'generators': [160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.8.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.e1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862768
    {'ambient': '2160.dm', 'aut_centralizer_order': 192, 'aut_label': '540.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '108.f1.a1', '180.m1.a1', '270.b1.a1', '270.d1.a1', '270.e1.a1'], 'contains': ['1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1093, -1, 9471, -1, 1091, -1, 9449, -1], 'generators': [288872, 120305], 'label': '2160.dm.540.f1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '60.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '540.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862769
    {'ambient': '2160.dm', 'aut_centralizer_order': 64, 'aut_label': '540.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.o1.a1', '108.g1.a1', '180.n1.a1', '270.b1.a1', '270.c1.a1', '270.c1.b1'], 'contains': ['1080.c1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1513, -1, 8848, -1, 1902, -1, 9261, -1], 'generators': [288872, 120329], 'label': '2160.dm.540.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '20.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '540.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862770
    {'ambient': '2160.dm', 'aut_centralizer_order': 1728, 'aut_label': '720.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.b1.a1', '240.b1.b1', '360.a1.a1', '360.c1.a1', '360.c1.b1', '360.g1.a1', '360.j1.a1', '360.j1.b1', '360.m1.a1'], 'contains': ['2160.a1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5920, 8406, 3975, 1217, 6283, 1965, 4202, 1977], 'generators': [30], 'label': '2160.dm.720.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '720.a1.a1', 'normal_contained_in': ['80.a1.a1', '144.a1.a1', '360.a1.a1'], 'normal_contains': ['2160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '360.132', 'quotient_action_kernel_order': 360, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862771
    {'ambient': '2160.dm', 'aut_centralizer_order': 432, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '360.b1.a1', '360.d1.a1', '360.f1.a1', '360.h1.a1', '360.i1.a1', '360.k1.a1', '360.n1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6182, -1, 2436, -1, 6965, -1, 2590, -1], 'generators': [328472], 'label': '2160.dm.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '720.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862772
    {'ambient': '2160.dm', 'aut_centralizer_order': 432, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.b1', '240.a1.a1', '240.b1.b1', '240.c1.b1', '360.b1.b1', '360.d1.b1', '360.f1.b1', '360.h1.b1', '360.i1.b1', '360.k1.b1', '360.n1.b1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6182, -1, 5528, -1, 6965, -1, 6507, -1], 'generators': [298233], 'label': '2160.dm.720.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '720.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862773
    {'ambient': '2160.dm', 'aut_centralizer_order': 216, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.b1.a1', '240.c1.a1', '240.c1.b1', '360.e1.a1', '360.l1.a1', '360.o1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9070, -1, 636, -1, 8813, -1, 2253, -1], 'generators': [328502], 'label': '2160.dm.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '720.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862774
    {'ambient': '2160.dm', 'aut_centralizer_order': 216, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '240.b1.b1', '240.c1.a1', '240.c1.b1', '360.e1.b1', '360.l1.b1', '360.o1.b1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9070, -1, 5233, -1, 8813, -1, 4109, -1], 'generators': [338582], 'label': '2160.dm.720.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '720.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 168862775
    {'ambient': '2160.dm', 'aut_centralizer_order': 1152, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.a1.a1', '360.b1.a1', '360.b1.b1', '540.a1.a1', '540.a1.b1', '540.b1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4566, -1, 3766, -1, 5455, -1, 4155, -1], 'generators': [54], 'label': '2160.dm.1080.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '1080.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862776
    {'ambient': '2160.dm', 'aut_centralizer_order': 288, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.c1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '540.a1.a1', '540.c1.a1', '540.d1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6574, -1, 2545, -1, 6888, -1, 2497, -1], 'generators': [288152], 'label': '2160.dm.1080.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '1080.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862777
    {'ambient': '2160.dm', 'aut_centralizer_order': 288, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.b1', '360.c1.b1', '360.d1.b1', '360.e1.b1', '360.f1.b1', '540.a1.b1', '540.c1.b1', '540.d1.b1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6574, -1, 5381, -1, 6888, -1, 6964, -1], 'generators': [160625], 'label': '2160.dm.1080.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '1080.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862778
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 18, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.b1.a1', '18.b1.b1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.e1.a1', '18.f1.a1', '27.a1.a1', '45.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [492, -1, 9603, -1, 690, -1, 7984, -1], 'generators': [54, 288872, 160649, 25866086400, 30, 288152], 'label': '2160.dm.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862779
    {'ambient': '2160.dm', 'aut_centralizer_order': 384, 'aut_label': '1080.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.g1.a1', '360.h1.a1', '360.h1.b1', '540.b1.a1', '540.d1.a1', '540.d1.b1', '540.e1.a1', '540.e1.b1', '540.f1.a1', '540.g1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2275, -1, 8147, -1, 2822, -1, 7106, -1], 'generators': [333513], 'label': '2160.dm.1080.c1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1080.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862780
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '360.i1.a1', '360.j1.a1', '360.k1.a1', '360.l1.a1', '540.a1.a1', '540.c1.a1', '540.e1.a1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5823, -1, 1624, -1, 7041, -1, 2544, -1], 'generators': [288206], 'label': '2160.dm.1080.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1080.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862781
    {'ambient': '2160.dm', 'aut_centralizer_order': 96, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.b1', '360.i1.b1', '360.j1.b1', '360.k1.b1', '360.l1.b1', '540.a1.b1', '540.c1.b1', '540.e1.b1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5823, -1, 6212, -1, 7041, -1, 6864, -1], 'generators': [160649], 'label': '2160.dm.1080.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '1080.d1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862782
    {'ambient': '2160.dm', 'aut_centralizer_order': 128, 'aut_label': '1080.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.m1.a1', '360.n1.a1', '360.n1.b1', '360.o1.a1', '360.o1.b1', '540.b1.a1', '540.c1.a1', '540.c1.b1'], 'contains': ['2160.a1.a1'], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7461, -1, 3942, -1, 7735, -1, 4048, -1], 'generators': [333567], 'label': '2160.dm.1080.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '1080.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862783
    {'ambient': '2160.dm', 'aut_centralizer_order': None, 'aut_label': '2160.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': ['432.a1.a1', '720.a1.a1', '720.b1.a1', '720.b1.b1', '720.c1.a1', '720.c1.b1', '1080.a1.a1', '1080.b1.a1', '1080.b1.b1', '1080.c1.a1', '1080.d1.a1', '1080.d1.b1', '1080.e1.a1'], 'contains': [], 'core': '2160.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6182, 7714, 3942, 1217, 6965, 2375, 4109, 2299], 'generators': [], 'label': '2160.dm.2160.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '2160.a1.a1', 'normal_contained_in': ['240.a1.a1', '432.a1.a1', '720.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '2160.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 168862784
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.b1.b1', '216.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '20.f1.a1', '20.g1.a1', '30.b1.a1', '30.d1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4081, 5323, 6649, 3187, 4504, 3289, 3771, 4058], 'generators': [54, 333513, 30, 328472, 338552, 288152], 'label': '2160.dm.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862785
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': ['1080.b1.a1', '1080.d1.a1', '1080.b1.b1', '1080.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '6.c1.a1', '10.b1.a1', '18.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1647, 6513, 8799, 2501, 2181, 2346, 8468, 2003], 'generators': [54, 333513, 25866086400, 120329, 30, 328472, 338552], 'label': '2160.dm.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862786
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.b1.a1', '216.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.b1', '20.c1.b1', '20.f1.b1', '20.g1.b1', '30.b1.b1', '30.d1.b1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4081, 5323, 7830, 5332, 4504, 3289, 7377, 2986], 'generators': [54, 333513, 160649, 30, 328472, 338552], 'label': '2160.dm.10.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.b1', 'normal_contained_in': ['2.a1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.b1', '20.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.b1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862801
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.l1.a1', '36.b1.a1', '36.d1.a1', '60.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5956, -1, 1566, -1, 6134, -1, 2413, -1], 'generators': [54, 25866086400, 30, 328472, 288152], 'label': '2160.dm.12.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': '12.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862787
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['216.b1.a1', '216.d1.a1', '216.b1.b1', '216.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.d1.a1', '20.e1.a1', '30.c1.a1', '90.c1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2102, 6601, 8843, 2414, 1916, 2634, 9336, 1216], 'generators': [54, 333513, 120329, 30, 328472, 338552], 'label': '2160.dm.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.d1.a1', '20.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862788
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.d1.a1', '216.a1.a1', '216.e1.a1', '216.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.c1.b1', '20.e1.a1', '30.e1.a1', '90.d1.a1'], 'core': '10.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2543, 4835, 8188, 6096, 3043, 4726, 8577, 2632], 'generators': [333513, 160649, 30, 328472, 338552, 288152], 'label': '2160.dm.10.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.a1', 'normal_contained_in': ['2.c1.a1', '5.a1.a1'], 'normal_contains': ['20.b1.a1', '20.c1.b1', '20.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862789
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.b1.a1', '216.a1.a1', '216.e1.a1', '216.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '5.a1.a1'], 'contains': ['20.b1.b1', '20.c1.a1', '20.e1.a1', '30.e1.b1', '90.d1.b1'], 'core': '10.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2543, 4835, 8611, 3943, 3043, 4726, 9091, 5862], 'generators': [30, 120329, 338552, 333513, 160673, 328472], 'label': '2160.dm.10.c1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.b1', 'normal_contained_in': ['2.c1.b1', '5.a1.a1'], 'normal_contains': ['20.b1.b1', '20.c1.a1', '20.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862790
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '10.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['216.d1.a1', '216.a1.a1', '216.e1.a1', '216.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.b1.b1', '20.d1.a1', '30.a1.a1', '90.e1.a1'], 'core': '10.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1475, 1869, 9018, 7332, 1116, 8438, 9200, 8775], 'generators': [333513, 30, 328472, 160673, 338552, 288152], 'label': '2160.dm.10.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.d1.a1', 'normal_contained_in': ['2.d1.a1', '5.a1.a1'], 'normal_contains': ['20.b1.a1', '20.b1.b1', '20.d1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862791
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '10.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['216.b1.a1', '216.a1.a1', '216.e1.a1', '216.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.c1.b1', '20.d1.a1', '30.f1.a1', '90.f1.a1'], 'core': '10.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1263, 3685, 9165, 4584, 899, 6346, 8996, 6405], 'generators': [288206, 333513, 160649, 30, 328472, 338552], 'label': '2160.dm.10.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.e1.a1', 'normal_contained_in': ['2.e1.a1', '5.a1.a1'], 'normal_contains': ['20.c1.b1', '20.c1.a1', '20.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862792
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': ['180.f1.b1', '180.h1.b1', '180.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '36.k1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3321, 2999, 7036, 9718, 3911, 7077, 3281, 7060], 'generators': [333513, 25866086400, 328472, 338552, 288152], 'label': '2160.dm.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862793
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': ['180.f1.a1', '180.h1.a1', '180.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.b1.b1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.g1.b1', '36.k1.b1', '60.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3321, 2999, 8004, 9036, 3911, 7077, 7071, 7636], 'generators': [333513, 25866086400, 160625, 328472, 338552], 'label': '2160.dm.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862794
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['180.f1.a1', '180.h1.a1', '180.d1.a1', '180.f1.b1', '180.h1.b1', '180.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '60.b1.a1', '108.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [944, 1131, 9373, 8263, 1749, 7910, 8789, 8291], 'generators': [120305, 333513, 25866086400, 328472, 338552], 'label': '2160.dm.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '432.741', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862795
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.k1.a1', '36.a1.a1', '36.b1.a1', '60.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5678, -1, 2630, -1, 6302, -1, 1197, -1], 'generators': [54, 25866086400, 328472, 338552, 288152], 'label': '2160.dm.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862796
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['1080.d1.a1', '1080.a1.a1', '1080.e1.a1', '1080.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.e1.a1', '6.e1.a1', '10.c1.a1', '18.d1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2680, 4546, 8134, 6970, 3123, 4160, 7503, 2850], 'generators': [333513, 160649, 25866086400, 30, 328472, 338552, 288152], 'label': '2160.dm.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.e1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862797
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.b1.b1'], 'contains': ['24.b1.a1', '24.g1.b1', '24.k1.b1', '36.a1.b1', '36.b1.b1', '60.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5678, -1, 5591, -1, 6302, -1, 5909, -1], 'generators': [54, 25866086400, 160679, 328472, 338552], 'label': '2160.dm.12.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.c1.b1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862798
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.o1.a1', '36.c1.a1', '36.c1.b1', '60.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3541, -1, 7143, -1, 5106, -1, 4596, -1], 'generators': [54, 333513, 25866086400, 328472, 338552], 'label': '2160.dm.12.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '432.741', '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': '72.40'}
  • id: 168862799
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.i1.a1', '36.a1.a1', '36.d1.a1', '60.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6119, -1, 1704, -1, 5965, -1, 2515, -1], 'generators': [54, 25866086400, 30, 5760, 288152], 'label': '2160.dm.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.e1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862800
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.d1.b1'], 'contains': ['24.c1.b1', '24.d1.b1', '24.i1.b1', '36.a1.b1', '36.d1.b1', '60.e1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6119, -1, 4781, -1, 5965, -1, 5648, -1], 'generators': [54, 160649, 25866086400, 298233, 30], 'label': '2160.dm.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.e1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862802
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '72.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.d1.b1'], 'contains': ['24.c1.b1', '24.e1.b1', '24.l1.b1', '36.b1.b1', '36.d1.b1', '60.f1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5956, -1, 4439, -1, 6134, -1, 5546, -1], 'generators': [54, 160649, 25866086400, 30, 338552], 'label': '2160.dm.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.f1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862803
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.h1.a1', '24.m1.a1', '36.c1.a1', '36.e1.a1', '60.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4317, -1, 2169, -1, 4921, -1, 3603, -1], 'generators': [54, 333513, 25866086400, 30, 328472], 'label': '2160.dm.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.g1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862804
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.b1'], 'contains': ['24.c1.b1', '24.h1.b1', '24.m1.b1', '36.c1.b1', '36.e1.a1', '60.g1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4317, -1, 6129, -1, 4921, -1, 4809, -1], 'generators': [54, 333513, 25866086400, 298233, 30], 'label': '2160.dm.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.g1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862805
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1'], 'contains': ['24.d1.a1', '24.l1.a1', '24.m1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '60.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8598, -1, 864, -1, 7871, -1, 1465, -1], 'generators': [333567, 25866086400, 328473, 30, 5760], 'label': '2160.dm.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.h1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862806
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.d1.b1'], 'contains': ['24.d1.b1', '24.l1.b1', '24.m1.b1', '36.f1.b1', '36.g1.b1', '36.h1.b1', '60.h1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8598, -1, 5177, -1, 7871, -1, 5179, -1], 'generators': [333567, 160649, 25866086400, 30, 338552], 'label': '2160.dm.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.h1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862807
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1728.46586', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['1080.b1.a1', '1080.a1.a1', '1080.e1.a1', '1080.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.e1.a1', '6.e1.b1', '10.c1.b1', '18.d1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2680, 4546, 8502, 4183, 3123, 4160, 7977, 5533], 'generators': [30, 120329, 338552, 333513, 160673, 25866086400, 328472], 'label': '2160.dm.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.a1', '4.e1.a1', '10.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862808
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1'], 'contains': ['24.e1.a1', '24.i1.a1', '24.m1.a1', '36.f1.a1', '36.j1.a1', '60.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8220, -1, 1357, -1, 6830, -1, 1979, -1], 'generators': [333567, 25866086400, 30, 328472, 288152], 'label': '2160.dm.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.i1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862809
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.d1.b1'], 'contains': ['24.e1.b1', '24.i1.b1', '24.m1.b1', '36.f1.b1', '36.j1.b1', '60.i1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8220, -1, 4957, -1, 6830, -1, 5292, -1], 'generators': [151889, 333567, 25866086400, 298233, 30], 'label': '2160.dm.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.i1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862810
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['24.f1.a1', '24.j1.a1', '24.n1.a1', '36.h1.a1', '36.j1.a1', '60.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9422, -1, 312, -1, 9488, -1, 334, -1], 'generators': [333567, 25866086400, 338582, 328472, 288152], 'label': '2160.dm.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '12.j1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862811
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1'], 'contains': ['24.f1.b1', '24.j1.b1', '24.n1.b1', '36.h1.b1', '36.j1.b1', '60.j1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9422, -1, 5368, -1, 9488, -1, 4709, -1], 'generators': [333567, 160649, 25866086400, 298233, 328502], 'label': '2160.dm.12.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.b1', 'old_label': '12.j1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862812
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.b1.a1'], 'contains': ['24.g1.a1', '24.k1.a1', '24.o1.a1', '36.g1.a1', '36.j1.a1', '60.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7230, -1, 2480, -1, 8279, -1, 963, -1], 'generators': [333567, 25866086400, 328472, 338552, 288152], 'label': '2160.dm.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862813
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.b1.b1'], 'contains': ['24.g1.b1', '24.k1.b1', '24.o1.a1', '36.g1.b1', '36.j1.b1', '60.k1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7230, -1, 5986, -1, 8279, -1, 5752, -1], 'generators': [333567, 25866086400, 160679, 328472, 338552], 'label': '2160.dm.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.k1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862814
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.h1.a1', '36.i1.a1', '36.k1.a1', '60.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5196, -1, 3435, -1, 4079, -1, 2813, -1], 'generators': [333513, 25866086400, 30, 328472, 288152], 'label': '2160.dm.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862815
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '72.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.d1.b1'], 'contains': ['24.d1.b1', '24.e1.b1', '24.h1.b1', '36.i1.b1', '36.k1.b1', '60.l1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5196, -1, 7274, -1, 4079, -1, 6869, -1], 'generators': [25866086400, 298233, 30, 160673, 5041], 'label': '2160.dm.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.l1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862816
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.d1.a1'], 'contains': ['24.h1.a1', '24.i1.a1', '24.l1.a1', '36.l1.a1', '36.o1.a1', '60.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4738, -1, 3720, -1, 4248, -1, 3062, -1], 'generators': [288206, 333513, 25866086400, 30, 328472], 'label': '2160.dm.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.m1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862817
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.143', 'aut_weyl_index': 24, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.d1.b1'], 'contains': ['24.h1.b1', '24.i1.b1', '24.l1.b1', '36.l1.b1', '36.o1.b1', '60.m1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4738, -1, 6703, -1, 4248, -1, 6613, -1], 'generators': [160649, 25866086400, 298233, 30, 5041], 'label': '2160.dm.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.m1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 168862818
    {'ambient': '2160.dm', 'aut_centralizer_order': 3, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.93925', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': ['1080.d1.a1', '1080.a1.a1', '1080.e1.a1', '1080.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.a1.a1', '10.d1.a1', '18.e1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1237, 1473, 9119, 8219, 1653, 7524, 8123, 7622], 'generators': [333513, 25866086400, 30, 328472, 160673, 338552, 288152], 'label': '2160.dm.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.a1.a1', '10.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862819
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.e1.b1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '36.o1.a1', '60.n1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3119, -1, 7508, -1, 3745, -1, 3704, -1], 'generators': [288206, 333513, 25866086400, 328472, 338552], 'label': '2160.dm.12.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862820
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.877', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.b1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.k1.b1', '36.o1.b1', '60.n1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3119, -1, 7414, -1, 3745, -1, 6971, -1], 'generators': [333513, 160649, 25866086400, 328472, 338552], 'label': '2160.dm.12.n1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862821
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.a1.a1', '60.o1.a1', '108.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2302, -1, 8348, -1, 2751, -1, 8410, -1], 'generators': [333513, 25866086400, 120329, 328472, 338552], 'label': '2160.dm.12.o1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862822
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.b1.b1', '30.c1.a1', '30.e1.a1', '30.e1.b1', '30.f1.a1', '135.a1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1650, -1, 8935, -1, 2382, -1, 8864, -1], 'generators': [54, 333513, 160679, 328472, 338552, 288152], 'label': '2160.dm.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862823
    {'ambient': '2160.dm', 'aut_centralizer_order': 27, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '128.1669', 'aut_weyl_index': 27, 'centralizer': '16.a1.a1', 'complements': ['135.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.e1.b1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.c1.a1', '48.c1.b1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7499, 8340, 2319, 1251, 8056, 2031, 3195, 2029], 'generators': [25866086400, 30, 328472, 338552], 'label': '2160.dm.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['48.a1.a1', '80.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.741', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 168862824
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.g1.a1', '36.j1.a1', '36.k1.a1', '36.o1.a1', '54.a1.a1', '90.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4676, -1, 2960, -1, 5335, -1, 2286, -1], 'generators': [54, 333513, 25866086400, 328472, 288152], 'label': '2160.dm.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862825
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.5', 'aut_weyl_index': 144, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.d1.b1'], 'contains': ['36.a1.b1', '36.b1.b1', '36.c1.b1', '36.g1.b1', '36.j1.b1', '36.k1.b1', '36.o1.b1', '54.a1.b1', '90.a1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4676, -1, 6586, -1, 5335, -1, 6486, -1], 'generators': [54, 25866086400, 298233, 160679, 5041], 'label': '2160.dm.18.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '18.a1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 168862826
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.f1.a1', '36.i1.a1', '36.l1.a1', '54.a1.a1', '90.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2735, -1, 6443, -1, 3022, -1, 4084, -1], 'generators': [54, 288872, 25866086400, 30, 288152], 'label': '2160.dm.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862827
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '9.a1.a1'], 'contains': ['36.d1.b1', '36.e1.a1', '36.f1.b1', '36.i1.b1', '36.l1.b1', '54.a1.b1', '90.b1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2735, -1, 7788, -1, 3022, -1, 6740, -1], 'generators': [54, 288872, 160649, 25866086400, 30], 'label': '2160.dm.18.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.b1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862828
    {'ambient': '2160.dm', 'aut_centralizer_order': 8, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.m1.a1', '36.n1.a1', '54.b1.a1', '90.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [755, -1, 9514, -1, 690, -1, 8673, -1], 'generators': [54, 288872, 25866086400, 120329, 30], 'label': '2160.dm.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 168862829
    {'ambient': '2160.dm', 'aut_centralizer_order': 1, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': ['1080.b1.a1', '1080.a1.a1', '1080.e1.a1', '1080.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1', '6.f1.a1', '10.e1.a1', '18.f1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [947, 2816, 9316, 5319, 1373, 6280, 7810, 6354], 'generators': [288206, 333513, 160649, 25866086400, 30, 328472, 338552], 'label': '2160.dm.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.c1.a1', '4.d1.a1', '10.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '432.741', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862830
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.206', 'aut_weyl_index': 36, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.l1.b1', '36.n1.a1', '54.c1.a1', '90.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1668, -1, 8641, -1, 2395, -1, 7795, -1], 'generators': [288872, 160649, 25866086400, 30, 288152], 'label': '2160.dm.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862831
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.206', 'aut_weyl_index': 36, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '9.a1.a1'], 'contains': ['36.i1.b1', '36.l1.a1', '36.n1.a1', '54.c1.b1', '90.d1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1668, -1, 9002, -1, 2395, -1, 8162, -1], 'generators': [288872, 25866086400, 120329, 30, 160673], 'label': '2160.dm.18.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862832
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.196', 'aut_weyl_index': 54, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.i1.b1', '36.m1.a1', '54.d1.a1', '90.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [75, -1, 9728, -1, 77, -1, 8269, -1], 'generators': [288872, 25866086400, 30, 160673, 288152], 'label': '2160.dm.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '432.741', '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': '8.5'}
  • id: 168862833
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 18, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '9.a1.a1'], 'contains': ['36.l1.a1', '36.l1.b1', '36.m1.a1', '54.e1.a1', '90.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [245, -1, 9922, -1, 476, -1, 8031, -1], 'generators': [288206, 288872, 160649, 25866086400, 30], 'label': '2160.dm.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 168862834
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.a1.b1', '10.b1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '60.d1.a1', '60.g1.a1', '60.g1.b1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4041, 7255, 7237, 2414, 4419, 2379, 6356, 2303], 'generators': [54, 333513, 30, 328472, 338552], 'label': '2160.dm.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.a1.b1', '10.b1.a1'], 'normal_contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862850
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 216, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.e1.a1', '12.h1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '120.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8762, -1, 736, -1, 7348, -1, 1199, -1], 'generators': [25866086400, 30, 5760, 288152], 'label': '2160.dm.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.d1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 168862835
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '20.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': ['108.c1.b1', '108.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1', '10.c1.a1', '10.d1.a1'], 'contains': ['40.b1.a1', '40.d1.a1', '60.a1.a1', '60.l1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3617, 4418, 7065, 7058, 3374, 5409, 3957, 4679], 'generators': [333513, 30, 328472, 338552, 288152], 'label': '2160.dm.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.b1.a1', '10.a1.a1', '10.c1.a1', '10.d1.a1'], 'normal_contains': ['40.b1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862836
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '20.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': ['108.c1.a1', '108.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.a1.b1', '10.c1.b1', '10.d1.a1'], 'contains': ['40.b1.a1', '40.d1.b1', '60.a1.b1', '60.l1.b1'], 'core': '20.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3617, 4418, 8074, 6323, 3374, 5409, 7667, 5751], 'generators': [333513, 30, 328472, 160673, 338552], 'label': '2160.dm.20.b1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.b1.b1', 'normal_contained_in': ['4.b1.b1', '10.a1.b1', '10.c1.b1', '10.d1.a1'], 'normal_contains': ['40.b1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.b1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862837
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['108.a1.b1', '108.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1', '10.c1.b1', '10.e1.a1'], 'contains': ['40.b1.a1', '40.e1.a1', '60.m1.a1', '60.n1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3299, 5425, 8185, 4026, 3220, 4726, 4204, 5215], 'generators': [288206, 333513, 30, 328472, 338552], 'label': '2160.dm.20.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.a1', 'normal_contained_in': ['4.c1.a1', '10.a1.a1', '10.c1.b1', '10.e1.a1'], 'normal_contains': ['40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862838
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['108.c1.a1', '108.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '10.a1.b1', '10.c1.a1', '10.e1.a1'], 'contains': ['40.b1.a1', '40.e1.b1', '60.m1.b1', '60.n1.b1'], 'core': '20.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3299, 5425, 7963, 5642, 3220, 4726, 7573, 3426], 'generators': [333513, 160649, 30, 328472, 338552], 'label': '2160.dm.20.c1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.b1', 'normal_contained_in': ['4.c1.b1', '10.a1.b1', '10.c1.a1', '10.e1.a1'], 'normal_contains': ['40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.b1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862839
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '20.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['108.c1.a1', '108.a1.a1', '108.c1.b1', '108.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.b1.a1', '10.d1.a1', '10.e1.a1'], 'contains': ['40.b1.a1', '60.b1.a1', '180.m1.a1'], 'core': '20.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1271, 2312, 9250, 4751, 1135, 6243, 9486, 6405], 'generators': [333513, 120353, 30, 328472, 338552], 'label': '2160.dm.20.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.d1.a1', 'normal_contained_in': ['4.d1.a1', '10.b1.a1', '10.d1.a1', '10.e1.a1'], 'normal_contains': ['40.b1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 168862840
    {'ambient': '2160.dm', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.e1.a1', '6.e1.b1', '6.f1.a1', '15.a1.a1', '27.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1486, -1, 8705, -1, 2460, -1, 7645, -1], 'generators': [54, 333513, 25866086400, 160679, 328472, 338552, 288152], 'label': '2160.dm.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '432.741', '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': '72.40'}
  • id: 168862841
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['108.c1.a1', '108.a1.a1', '108.c1.b1', '108.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.b1.a1', '10.c1.a1', '10.c1.b1'], 'contains': ['40.b1.a1', '60.o1.a1', '180.n1.a1'], 'core': '20.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2542, 6442, 8476, 3396, 2185, 3133, 9221, 2894], 'generators': [333513, 120329, 30, 328472, 338552], 'label': '2160.dm.20.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.e1.a1', 'normal_contained_in': ['4.e1.a1', '10.b1.a1', '10.c1.a1', '10.c1.b1'], 'normal_contains': ['40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '2160.dm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 168862842
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.d1.a1', '40.e1.a1', '60.c1.a1', '60.e1.a1', '60.f1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5773, -1, 2597, -1, 5544, -1, 2618, -1], 'generators': [54, 30, 328472, 338552, 288152], 'label': '2160.dm.20.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862843
    {'ambient': '2160.dm', 'aut_centralizer_order': 12, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '144.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '10.a1.b1'], 'contains': ['40.a1.a1', '40.d1.b1', '40.e1.b1', '60.c1.b1', '60.e1.b1', '60.f1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5773, -1, 5506, -1, 5544, -1, 7279, -1], 'generators': [54, 160649, 30, 328472, 338552], 'label': '2160.dm.20.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '20.f1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 168862844
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.162', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.d1.a1', '40.e1.a1', '60.h1.a1', '60.i1.a1', '60.j1.a1', '60.k1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6251, -1, 2390, -1, 7681, -1, 1858, -1], 'generators': [333567, 30, 328472, 338552, 288152], 'label': '2160.dm.20.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 168862845
    {'ambient': '2160.dm', 'aut_centralizer_order': 4, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.162', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '10.a1.b1'], 'contains': ['40.c1.a1', '40.d1.b1', '40.e1.b1', '60.h1.b1', '60.i1.b1', '60.j1.b1', '60.k1.b1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6251, -1, 6642, -1, 7681, -1, 7175, -1], 'generators': [333567, 160649, 30, 328472, 338552], 'label': '2160.dm.20.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '20.g1.b1', 'projective_image': '2160.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 168862846
    {'ambient': '2160.dm', 'aut_centralizer_order': 6, 'aut_label': '24.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '576.8289', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1', '12.d1.a1', '12.n1.a1', '12.n1.b1', '12.o1.a1'], 'contains': ['48.a1.a1', '72.h1.a1', '72.h1.b1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3061, 3848, 7475, 8263, 3480, 4886, 6483, 6672], 'generators': [333513, 25866086400, 328472, 338552], 'label': '2160.dm.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 168862847
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.119', 'aut_weyl_index': 54, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.c1.b1', '12.d1.a1'], 'contains': ['48.a1.a1', '72.b1.a1', '72.b1.b1', '120.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5365, -1, 3636, -1, 5884, -1, 3574, -1], 'generators': [54, 25866086400, 328472, 338552], 'label': '2160.dm.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '432.741', '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': '8.3'}
  • id: 168862848
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.b1.a1', '120.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4859, -1, 1763, -1, 5396, -1, 2839, -1], 'generators': [54, 25866086400, 30, 328472], 'label': '2160.dm.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '432.741', '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': '12.4'}
  • id: 168862849
    {'ambient': '2160.dm', 'aut_centralizer_order': 18, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 72, 'centralizer': '24.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.e1.b1', '12.f1.b1', '12.g1.b1'], 'contains': ['48.b1.b1', '72.a1.a1', '72.b1.b1', '120.c1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4859, -1, 3735, -1, 5396, -1, 4705, -1], 'generators': [54, 25866086400, 298233, 30], 'label': '2160.dm.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.c1.b1', 'projective_image': '432.741', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}