Abstract group data - 240.60

Formats: - HTML - YAML - JSON - 2025-11-15T14:30:47.050392

• 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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 4, 12], 'aut_gens': [[1, 2, 16], [5, 6, 16], [1, 10, 16], [1, 2, 176], [1, 2, 208], [13, 162, 64]], 'aut_group': '384.18344', 'aut_hash': 18344, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 13, 'aut_perms': [6, 1, 39916801, 811566, 518918694], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 4, 2, 1], [8, 6, 2, 1], [10, 1, 4, 1], [10, 4, 4, 1], [10, 12, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [20, 2, 4, 1], [30, 2, 4, 1], [30, 4, 8, 1], [40, 6, 8, 1], [60, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times D_4\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 1], [2, 12, 1], [3, 2, 1], [4, 2, 1], [5, 1, 4], [6, 2, 1], [6, 4, 2], [8, 6, 2], [10, 1, 4], [10, 4, 4], [10, 12, 4], [12, 4, 1], [15, 2, 4], [20, 2, 4], [30, 2, 4], [30, 4, 8], [40, 6, 8], [60, 4, 4]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 60, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['48.15', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 4, 2, 1], [8, 6, 2, 1], [10, 1, 4, 1], [10, 4, 4, 1], [10, 12, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [20, 2, 4, 1], [30, 2, 4, 1], [30, 4, 8, 1], [40, 6, 8, 1], [60, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 120, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '60.11', 'hash': 60, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 14, 16], [5, 2, 176], [1, 82, 16]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 20], [2, 35], [4, 5]], 'label': '240.60', 'linC_count': 196, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 64, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:D8', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 60, 'number_divisions': 20, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 44, 'number_subgroup_classes': 44, 'number_subgroups': 112, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 17], [3, 2], [4, 2], [5, 4], [6, 10], [8, 12], [10, 68], [12, 4], [15, 8], [20, 8], [30, 40], [40, 48], [60, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 4, 0], 'outer_gens': [[1, 10, 16], [13, 2, 16], [1, 2, 208]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 7], [8, 3], [16, 3]], 'representations': {'PC': {'code': 27575784872951778074631, 'gens': [1, 2, 5], 'pres': [6, -2, -2, -2, -2, -3, -5, 169, 31, 218, 50, 2650, 118]}, 'GLZN': {'d': 2, 'p': 62, 'gens': [238389, 11201463, 359446, 14538069, 7573951, 1052508]}, 'Perm': {'d': 16, 'gens': [87178296556, 2813, 522910080, 13307, 19342, 1394852659200]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:D_8', 'transitive_degree': 120, '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: 109363408
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 60, 'group_order': 240, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109363419
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 60, 'group_order': 240, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8, 'size': 1}
  • id: 109363430
    {'aut_label': '2B', 'centralizer': '4.b1.a1', 'counter': 3, 'group_counter': 60, 'group_order': 240, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 1, 'size': 4}
  • id: 109363441
    {'aut_label': '2C', 'centralizer': '12.c1.a1', 'counter': 4, 'group_counter': 60, 'group_order': 240, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 3, 'size': 12}
  • id: 109363452
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 60, 'group_order': 240, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 160, 'size': 2}
  • id: 109363463
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 6, 'group_counter': 60, 'group_order': 240, 'label': '4A', 'order': 4, 'powers': [2, 6, 6], 'representative': 4, 'size': 2}
  • id: 109363465
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 60, 'group_order': 240, 'label': '5A1', 'order': 5, 'powers': [9, 10, 1], 'representative': 96, 'size': 1}
  • id: 109363466
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 60, 'group_order': 240, 'label': '5A-1', 'order': 5, 'powers': [10, 9, 1], 'representative': 144, 'size': 1}
  • id: 109363467
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 60, 'group_order': 240, 'label': '5A2', 'order': 5, 'powers': [8, 7, 1], 'representative': 192, 'size': 1}
  • id: 109363409
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 60, 'group_order': 240, 'label': '5A-2', 'order': 5, 'powers': [7, 8, 1], 'representative': 48, 'size': 1}
  • id: 109363410
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 60, 'group_order': 240, 'label': '6A', 'order': 6, 'powers': [5, 2, 11], 'representative': 168, 'size': 2}
  • id: 109363411
    {'aut_label': '6B1', 'centralizer': '4.b1.a1', 'counter': 12, 'group_counter': 60, 'group_order': 240, 'label': '6B1', 'order': 6, 'powers': [5, 3, 13], 'representative': 81, 'size': 4}
  • id: 109363412
    {'aut_label': '6B1', 'centralizer': '4.b1.a1', 'counter': 13, 'group_counter': 60, 'group_order': 240, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 12], 'representative': 161, 'size': 4}
  • id: 109363413
    {'aut_label': '8A1', 'centralizer': '6.c1.a1', 'counter': 14, 'group_counter': 60, 'group_order': 240, 'label': '8A1', 'order': 8, 'powers': [6, 15, 15], 'representative': 10, 'size': 6}
  • id: 109363414
    {'aut_label': '8A1', 'centralizer': '6.c1.a1', 'counter': 15, 'group_counter': 60, 'group_order': 240, 'label': '8A3', 'order': 8, 'powers': [6, 14, 14], 'representative': 14, 'size': 6}
  • id: 109363415
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 60, 'group_order': 240, 'label': '10A1', 'order': 10, 'powers': [8, 18, 2], 'representative': 200, 'size': 1}
  • id: 109363416
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 60, 'group_order': 240, 'label': '10A-1', 'order': 10, 'powers': [7, 19, 2], 'representative': 56, 'size': 1}
  • id: 109363417
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 60, 'group_order': 240, 'label': '10A3', 'order': 10, 'powers': [9, 17, 2], 'representative': 104, 'size': 1}
  • id: 109363418
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 60, 'group_order': 240, 'label': '10A-3', 'order': 10, 'powers': [10, 16, 2], 'representative': 152, 'size': 1}
  • id: 109363420
    {'aut_label': '10B1', 'centralizer': '4.b1.a1', 'counter': 20, 'group_counter': 60, 'group_order': 240, 'label': '10B1', 'order': 10, 'powers': [7, 22, 3], 'representative': 49, 'size': 4}
  • id: 109363421
    {'aut_label': '10B1', 'centralizer': '4.b1.a1', 'counter': 21, 'group_counter': 60, 'group_order': 240, 'label': '10B-1', 'order': 10, 'powers': [8, 23, 3], 'representative': 193, 'size': 4}
  • id: 109363422
    {'aut_label': '10B1', 'centralizer': '4.b1.a1', 'counter': 22, 'group_counter': 60, 'group_order': 240, 'label': '10B3', 'order': 10, 'powers': [10, 21, 3], 'representative': 145, 'size': 4}
  • id: 109363423
    {'aut_label': '10B1', 'centralizer': '4.b1.a1', 'counter': 23, 'group_counter': 60, 'group_order': 240, 'label': '10B-3', 'order': 10, 'powers': [9, 20, 3], 'representative': 97, 'size': 4}
  • id: 109363424
    {'aut_label': '10C1', 'centralizer': '12.c1.a1', 'counter': 24, 'group_counter': 60, 'group_order': 240, 'label': '10C1', 'order': 10, 'powers': [7, 26, 4], 'representative': 51, 'size': 12}
  • id: 109363425
    {'aut_label': '10C1', 'centralizer': '12.c1.a1', 'counter': 25, 'group_counter': 60, 'group_order': 240, 'label': '10C-1', 'order': 10, 'powers': [8, 27, 4], 'representative': 35, 'size': 12}
  • id: 109363426
    {'aut_label': '10C1', 'centralizer': '12.c1.a1', 'counter': 26, 'group_counter': 60, 'group_order': 240, 'label': '10C3', 'order': 10, 'powers': [10, 25, 4], 'representative': 147, 'size': 12}
  • id: 109363427
    {'aut_label': '10C1', 'centralizer': '12.c1.a1', 'counter': 27, 'group_counter': 60, 'group_order': 240, 'label': '10C-3', 'order': 10, 'powers': [9, 24, 4], 'representative': 19, 'size': 12}
  • id: 109363428
    {'aut_label': '12A', 'centralizer': '4.a1.a1', 'counter': 28, 'group_counter': 60, 'group_order': 240, 'label': '12A', 'order': 12, 'powers': [11, 6, 28], 'representative': 84, 'size': 4}
  • id: 109363429
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 60, 'group_order': 240, 'label': '15A1', 'order': 15, 'powers': [31, 7, 5], 'representative': 32, 'size': 2}
  • id: 109363431
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 60, 'group_order': 240, 'label': '15A-1', 'order': 15, 'powers': [32, 8, 5], 'representative': 208, 'size': 2}
  • id: 109363432
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 31, 'group_counter': 60, 'group_order': 240, 'label': '15A2', 'order': 15, 'powers': [30, 9, 5], 'representative': 64, 'size': 2}
  • id: 109363433
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 32, 'group_counter': 60, 'group_order': 240, 'label': '15A-2', 'order': 15, 'powers': [29, 10, 5], 'representative': 176, 'size': 2}
  • id: 109363434
    {'aut_label': '20A1', 'centralizer': '2.c1.a1', 'counter': 33, 'group_counter': 60, 'group_order': 240, 'label': '20A1', 'order': 20, 'powers': [16, 35, 6], 'representative': 100, 'size': 2}
  • id: 109363435
    {'aut_label': '20A1', 'centralizer': '2.c1.a1', 'counter': 34, 'group_counter': 60, 'group_order': 240, 'label': '20A-1', 'order': 20, 'powers': [17, 36, 6], 'representative': 156, 'size': 2}
  • id: 109363436
    {'aut_label': '20A1', 'centralizer': '2.c1.a1', 'counter': 35, 'group_counter': 60, 'group_order': 240, 'label': '20A3', 'order': 20, 'powers': [18, 34, 6], 'representative': 60, 'size': 2}
  • id: 109363437
    {'aut_label': '20A1', 'centralizer': '2.c1.a1', 'counter': 36, 'group_counter': 60, 'group_order': 240, 'label': '20A-3', 'order': 20, 'powers': [19, 33, 6], 'representative': 196, 'size': 2}
  • id: 109363438
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 37, 'group_counter': 60, 'group_order': 240, 'label': '30A1', 'order': 30, 'powers': [31, 18, 11], 'representative': 40, 'size': 2}
  • id: 109363439
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 38, 'group_counter': 60, 'group_order': 240, 'label': '30A-1', 'order': 30, 'powers': [32, 19, 11], 'representative': 216, 'size': 2}
  • id: 109363440
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 39, 'group_counter': 60, 'group_order': 240, 'label': '30A7', 'order': 30, 'powers': [30, 16, 11], 'representative': 232, 'size': 2}
  • id: 109363442
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 40, 'group_counter': 60, 'group_order': 240, 'label': '30A-7', 'order': 30, 'powers': [29, 17, 11], 'representative': 24, 'size': 2}
  • id: 109363443
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 41, 'group_counter': 60, 'group_order': 240, 'label': '30B1', 'order': 30, 'powers': [29, 20, 12], 'representative': 17, 'size': 4}
  • id: 109363444
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 42, 'group_counter': 60, 'group_order': 240, 'label': '30B-1', 'order': 30, 'powers': [30, 21, 13], 'representative': 225, 'size': 4}
  • id: 109363445
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 43, 'group_counter': 60, 'group_order': 240, 'label': '30B7', 'order': 30, 'powers': [31, 23, 12], 'representative': 113, 'size': 4}
  • id: 109363446
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 44, 'group_counter': 60, 'group_order': 240, 'label': '30B-7', 'order': 30, 'powers': [32, 22, 13], 'representative': 129, 'size': 4}
  • id: 109363447
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 45, 'group_counter': 60, 'group_order': 240, 'label': '30B11', 'order': 30, 'powers': [29, 20, 13], 'representative': 21, 'size': 4}
  • id: 109363448
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 46, 'group_counter': 60, 'group_order': 240, 'label': '30B-11', 'order': 30, 'powers': [30, 21, 12], 'representative': 65, 'size': 4}
  • id: 109363449
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 47, 'group_counter': 60, 'group_order': 240, 'label': '30B13', 'order': 30, 'powers': [32, 22, 12], 'representative': 209, 'size': 4}
  • id: 109363450
    {'aut_label': '30B1', 'centralizer': '4.b1.a1', 'counter': 48, 'group_counter': 60, 'group_order': 240, 'label': '30B-13', 'order': 30, 'powers': [31, 23, 13], 'representative': 33, 'size': 4}
  • id: 109363451
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 49, 'group_counter': 60, 'group_order': 240, 'label': '40A1', 'order': 40, 'powers': [33, 51, 14], 'representative': 50, 'size': 6}
  • id: 109363453
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 50, 'group_counter': 60, 'group_order': 240, 'label': '40A-1', 'order': 40, 'powers': [34, 52, 14], 'representative': 34, 'size': 6}
  • id: 109363454
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 51, 'group_counter': 60, 'group_order': 240, 'label': '40A3', 'order': 40, 'powers': [35, 50, 15], 'representative': 154, 'size': 6}
  • id: 109363455
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 52, 'group_counter': 60, 'group_order': 240, 'label': '40A-3', 'order': 40, 'powers': [36, 49, 15], 'representative': 26, 'size': 6}
  • id: 109363456
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 53, 'group_counter': 60, 'group_order': 240, 'label': '40A7', 'order': 40, 'powers': [36, 55, 14], 'representative': 18, 'size': 6}
  • id: 109363457
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 54, 'group_counter': 60, 'group_order': 240, 'label': '40A-7', 'order': 40, 'powers': [35, 56, 14], 'representative': 146, 'size': 6}
  • id: 109363458
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 55, 'group_counter': 60, 'group_order': 240, 'label': '40A11', 'order': 40, 'powers': [33, 54, 15], 'representative': 58, 'size': 6}
  • id: 109363459
    {'aut_label': '40A1', 'centralizer': '6.c1.a1', 'counter': 56, 'group_counter': 60, 'group_order': 240, 'label': '40A-11', 'order': 40, 'powers': [34, 53, 15], 'representative': 42, 'size': 6}
  • id: 109363460
    {'aut_label': '60A1', 'centralizer': '4.a1.a1', 'counter': 57, 'group_counter': 60, 'group_order': 240, 'label': '60A1', 'order': 60, 'powers': [37, 35, 28], 'representative': 20, 'size': 4}
  • id: 109363461
    {'aut_label': '60A1', 'centralizer': '4.a1.a1', 'counter': 58, 'group_counter': 60, 'group_order': 240, 'label': '60A-1', 'order': 60, 'powers': [38, 36, 28], 'representative': 68, 'size': 4}
  • id: 109363462
    {'aut_label': '60A1', 'centralizer': '4.a1.a1', 'counter': 59, 'group_counter': 60, 'group_order': 240, 'label': '60A7', 'order': 60, 'powers': [39, 33, 28], 'representative': 36, 'size': 4}
  • id: 109363464
    {'aut_label': '60A1', 'centralizer': '4.a1.a1', 'counter': 60, 'group_counter': 60, 'group_order': 240, 'label': '60A-7', 'order': 60, 'powers': [40, 34, 28], 'representative': 132, 'size': 4}
• 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: 4240560
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1a', '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], 'schur_index': 1}
  • id: 4240571
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1b', '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], 'schur_index': 1}
  • id: 4240573
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1c', '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], 'schur_index': 1}
  • id: 4240574
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1d', '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], 'schur_index': 1}
  • id: 4240579
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, -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: 4240561
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
  • id: 4240562
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, 2, 2, 2, 2, 2, -1, 1, 1, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, -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: 4240575
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1e', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, -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], 'schur_index': 1}
  • id: 4240576
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1f', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -1, -1, -1, -1, 4, -4, -4, 4, 4, -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], 'schur_index': 1}
  • id: 4240577
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1g', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 4, 4, -1, -1, -1, -1, 4, -4, -4, -4, -4, -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], 'schur_index': 1}
  • id: 4240578
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 4, 4, -1, -1, -1, -1, 4, 4, 4, -4, -4, -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], 'schur_index': 1}
  • id: 4240563
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2d', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 0, 4, 4, 4, 4, -4, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 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], 'schur_index': 1}
  • id: 4240564
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2e', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -2, -4, 4, 4, 4, 4, -2, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -4, -4, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4240570
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.4a', 'multiplicity': 1, 'nt': [24, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, 0, 4, 4, 4, 4, 2, 0, 0, 0, 0, -4, -4, -4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4240565
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2f', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 8, 8, 0, -4, 8, -2, -2, -2, -2, -4, -4, -4, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -4, 1, 1, 1, 1, -2, -2, -2, -2, 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: 4240566
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2g', 'multiplicity': 4, 'nt': [20, 12], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, -8, -2, -2, -2, -2, 8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -8, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4240567
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2h', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, -8, 0, -4, 8, -2, -2, -2, -2, -4, 4, 4, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, -4, 1, 1, 1, 1, -2, -2, -2, -2, 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: 4240568
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2i', 'multiplicity': 8, 'nt': [40, 50], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 16, 0, -4, -4, -4, -4, -16, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 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], 'schur_index': 1}
  • id: 4240569
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.2j', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, 0, 0, -8, -16, -4, -4, -4, -4, -8, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
  • id: 4240572
    {'cdim': 4, 'counter': 20, 'faithful': True, 'group': '240.60', 'group_order': 240, 'image': None, 'label': '240.60.4b', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -8, 0, -4, -4, -4, -4, 8, 0, 0, 0, 0, 4, 4, 4, 4, 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, 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: 6271105
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 240, 'label': '240.60.1a', '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]]]}
  • id: 6271116
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 120, 'label': '240.60.1b', '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]]]}
  • id: 6271127
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 120, 'label': '240.60.1c', '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]]]}
  • id: 6271138
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 120, 'label': '240.60.1d', '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]]]}
  • id: 6271149
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 48, 'label': '240.60.1e1', 'nt': [5, 1], 'q_character': None, 'values': [[[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, 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, 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, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]]]}
  • id: 6271160
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 48, 'label': '240.60.1e2', 'nt': [5, 4], 'q_character': None, 'values': [[[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, -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, -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, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]]]}
  • id: 6271162
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 48, 'label': '240.60.1e3', 'nt': [5, 1], 'q_character': None, 'values': [[[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, -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, -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, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]]]}
  • id: 6271163
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 48, 'label': '240.60.1e4', 'nt': [5, 4], 'q_character': None, 'values': [[[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, 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, 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, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]]]}
  • id: 6271164
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 24, 'label': '240.60.1f1', 'nt': [10, 1], 'q_character': None, 'values': [[[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, 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, 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, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]]]}
  • id: 6271106
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 24, 'label': '240.60.1f2', 'nt': [10, 4], 'q_character': None, 'values': [[[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, -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, -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, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]]]}
  • id: 6271107
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 24, 'label': '240.60.1f3', 'nt': [10, 1], 'q_character': None, 'values': [[[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, -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, -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, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]]]}
  • id: 6271108
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 24, 'label': '240.60.1f4', 'nt': [10, 4], 'q_character': None, 'values': [[[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, 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, 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, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]]]}
  • id: 6271109
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 24, 'label': '240.60.1g1', 'nt': [10, 1], 'q_character': None, 'values': [[[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, 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, 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, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]]]}
  • id: 6271110
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 24, 'label': '240.60.1g2', 'nt': [10, 4], 'q_character': None, 'values': [[[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, -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, -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, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]]]}
  • id: 6271111
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 24, 'label': '240.60.1g3', 'nt': [10, 1], 'q_character': None, 'values': [[[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, -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, -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, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]]]}
  • id: 6271112
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 24, 'label': '240.60.1g4', 'nt': [10, 4], 'q_character': None, 'values': [[[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, 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, 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, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]]]}
  • id: 6271113
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 24, 'label': '240.60.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[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, 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, 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, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]]]}
  • id: 6271114
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 24, 'label': '240.60.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[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, -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, -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, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]]]}
  • id: 6271115
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 24, 'label': '240.60.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[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, -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, -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, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]]]}
  • id: 6271117
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 24, 'label': '240.60.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[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, 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, 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, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]]]}
  • id: 6271118
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 40, 'label': '240.60.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-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: 6271119
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 60, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 30, 'label': '240.60.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]]]}
  • id: 6271120
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 20, 'label': '240.60.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-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: 6271121
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 24, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 15, 'label': '240.60.2d1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-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]], [[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, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271122
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 25, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 15, 'label': '240.60.2d2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-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]], [[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, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271123
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 10, 'label': '240.60.2e1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[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]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[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: 6271124
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 10, 'label': '240.60.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[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]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[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: 6271125
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 28, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 8, 'label': '240.60.2f1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-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]]]}
  • id: 6271126
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 29, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 8, 'label': '240.60.2f2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-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]]]}
  • id: 6271128
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 30, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 8, 'label': '240.60.2f3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-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]]]}
  • id: 6271129
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 31, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 8, 'label': '240.60.2f4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-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]]]}
  • id: 6271130
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 60, 'counter': 32, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 6, 'label': '240.60.2g1', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 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, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]]]}
  • id: 6271131
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 60, 'counter': 33, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 6, 'label': '240.60.2g2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 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, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]]]}
  • id: 6271132
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 60, 'counter': 34, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 6, 'label': '240.60.2g3', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 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, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]]]}
  • id: 6271133
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 60, 'counter': 35, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 6, 'label': '240.60.2g4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 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, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]]]}
  • id: 6271134
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 36, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.60.2h1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[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]]]}
  • id: 6271135
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 37, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.60.2h2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[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]]]}
  • id: 6271136
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 38, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.60.2h3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[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]]]}
  • id: 6271137
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 39, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.60.2h4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[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]]]}
  • id: 6271139
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 40, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i1', 'nt': [40, 50], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 4]], [[2, 16]], [[2, 8]], [[-2, 12]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-2, 8]], [[2, 12]], [[2, 4]], [[-2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8]], [[-2, 12]], [[2, 16]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16]], [[2, 12]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 11]], [[1, 3], [1, 13]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[-1, 3], [-1, 13]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[-1, 1], [1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271140
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 41, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i2', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 16]], [[-2, 4]], [[-2, 12]], [[2, 8]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[2, 12]], [[-2, 8]], [[-2, 16]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 8]], [[-2, 4]], [[2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 8]], [[-2, 16]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[-1, 3], [-1, 13]], [[1, 3], [1, 13]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[1, 1], [-1, 11]], [[-1, 1], [1, 11]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271141
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 42, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i3', 'nt': [40, 50], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 4]], [[2, 16]], [[2, 8]], [[-2, 12]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-2, 8]], [[2, 12]], [[2, 4]], [[-2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8]], [[-2, 12]], [[2, 16]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16]], [[2, 12]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 11]], [[-1, 3], [-1, 13]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[1, 3], [1, 13]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[1, 1], [-1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271142
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 43, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i4', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 16]], [[-2, 4]], [[-2, 12]], [[2, 8]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[2, 12]], [[-2, 8]], [[-2, 16]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 8]], [[-2, 4]], [[2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 8]], [[-2, 16]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[1, 3], [1, 13]], [[-1, 3], [-1, 13]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[-1, 1], [1, 11]], [[1, 1], [-1, 11]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271143
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 44, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i5', 'nt': [40, 50], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 12]], [[2, 8]], [[-2, 4]], [[2, 16]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[2, 4]], [[-2, 16]], [[2, 12]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 16]], [[2, 8]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[-2, 16]], [[2, 12]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 13]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [-1, 11]], [[-1, 1], [1, 11]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[1, 3], [1, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271144
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 45, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i6', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 8]], [[-2, 12]], [[2, 16]], [[-2, 4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-2, 16]], [[2, 4]], [[-2, 8]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 16]], [[-2, 4]], [[-2, 12]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12]], [[2, 4]], [[-2, 8]], [[-2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[-1, 1], [1, 11]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [-1, 11]], [[-1, 3], [-1, 13]], [[1, 3], [1, 13]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271145
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 46, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i7', 'nt': [40, 50], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 12]], [[2, 8]], [[-2, 4]], [[2, 16]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[2, 4]], [[-2, 16]], [[2, 12]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 16]], [[2, 8]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[-2, 16]], [[2, 12]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 13]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [1, 11]], [[1, 1], [-1, 11]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[-1, 3], [-1, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271146
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 30, 'counter': 47, 'cyclotomic_n': 40, 'dim': 2, 'faithful': False, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '80.25', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.60.2i8', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 8]], [[-2, 12]], [[2, 16]], [[-2, 4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-2, 16]], [[2, 4]], [[-2, 8]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 16]], [[-2, 4]], [[-2, 12]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12]], [[2, 4]], [[-2, 8]], [[-2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 5], [-1, 7], [1, 9], [-1, 13]], [[1, 1], [-1, 11]], [[-1, 3], [1, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 3], [-1, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [1, 11]], [[1, 3], [1, 13]], [[-1, 3], [-1, 13]], [[-1, 1], [1, 5], [1, 7], [-1, 9], [1, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6271147
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 48, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j1', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, -6]], [[2, 6]], [[2, 3]], [[2, -3]], [[-1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 6]], [[-1, -6]], [[-2, 3]], [[-2, -3]], [[-2, 6]], [[-2, -6]], [[-1, 6]], [[-1, -3]], [[-1, -6]], [[-1, 3]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[2, 1], [1, 6]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-2, 1], [-1, 6]], [[-1, 2], [1, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, 2], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -6]], [[1, 6]], [[1, 3]], [[1, -3]]]}
  • id: 6271148
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 49, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j2', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 6]], [[2, -6]], [[2, -3]], [[2, 3]], [[-1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 6]], [[2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -6]], [[-1, 6]], [[-2, -3]], [[-2, 3]], [[-2, -6]], [[-2, 6]], [[-1, -6]], [[-1, 3]], [[-1, 6]], [[-1, -3]], [[2, 1], [1, 6]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[1, 2], [-1, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[-2, 1], [-1, 6]], [[-1, 2], [1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[1, -6]], [[1, -3]], [[1, 3]]]}
  • id: 6271150
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 50, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, -6]], [[2, 6]], [[2, 3]], [[2, -3]], [[-1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 6]], [[-1, -6]], [[-2, 3]], [[-2, -3]], [[-2, 6]], [[-2, -6]], [[-1, 6]], [[-1, -3]], [[-1, -6]], [[-1, 3]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-2, 1], [-1, 6]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[2, 1], [1, 6]], [[1, 2], [-1, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-1, 2], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -6]], [[1, 6]], [[1, 3]], [[1, -3]]]}
  • id: 6271151
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 51, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j4', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 6]], [[2, -6]], [[2, -3]], [[2, 3]], [[-1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 6]], [[2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -3]], [[-1, 3]], [[-1, -6]], [[-1, 6]], [[-2, -3]], [[-2, 3]], [[-2, -6]], [[-2, 6]], [[-1, -6]], [[-1, 3]], [[-1, 6]], [[-1, -3]], [[-2, 1], [-1, 6]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-1, 2], [1, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[2, 1], [1, 6]], [[1, 2], [-1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[1, -6]], [[1, -3]], [[1, 3]]]}
  • id: 6271152
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 52, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j5', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, -3]], [[2, 3]], [[2, -6]], [[2, 6]], [[-1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[0, 0]], [[0, 0]], [[2, -6]], [[2, 6]], [[2, -3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -6]], [[-1, 6]], [[-1, 3]], [[-1, -3]], [[-2, -6]], [[-2, 6]], [[-2, 3]], [[-2, -3]], [[-1, 3]], [[-1, 6]], [[-1, -3]], [[-1, -6]], [[1, 2], [-1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[2, 1], [1, 6]], [[-1, 2], [1, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[-2, 1], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -3]], [[1, 3]], [[1, -6]], [[1, 6]]]}
  • id: 6271153
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 53, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j6', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 3]], [[2, -3]], [[2, 6]], [[2, -6]], [[-1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, -6]], [[2, 3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 6]], [[-1, -6]], [[-1, -3]], [[-1, 3]], [[-2, 6]], [[-2, -6]], [[-2, -3]], [[-2, 3]], [[-1, -3]], [[-1, -6]], [[-1, 3]], [[-1, 6]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, 2], [-1, 7]], [[-2, 1], [-1, 6]], [[-1, 2], [1, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[2, 1], [1, 6]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[1, -3]], [[1, 6]], [[1, -6]]]}
  • id: 6271154
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 54, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j7', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, -3]], [[2, 3]], [[2, -6]], [[2, 6]], [[-1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[0, 0]], [[0, 0]], [[2, -6]], [[2, 6]], [[2, -3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -6]], [[-1, 6]], [[-1, 3]], [[-1, -3]], [[-2, -6]], [[-2, 6]], [[-2, 3]], [[-2, -3]], [[-1, 3]], [[-1, 6]], [[-1, -3]], [[-1, -6]], [[-1, 2], [1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-2, 1], [-1, 6]], [[1, 2], [-1, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[2, 1], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -3]], [[1, 3]], [[1, -6]], [[1, 6]]]}
  • id: 6271155
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 20, 'counter': 55, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.60.2j8', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 3]], [[2, -3]], [[2, 6]], [[2, -6]], [[-1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, -6]], [[2, 3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 6]], [[-1, -6]], [[-1, -3]], [[-1, 3]], [[-2, 6]], [[-2, -6]], [[-2, -3]], [[-2, 3]], [[-1, -3]], [[-1, -6]], [[-1, 3]], [[-1, 6]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[-1, 2], [1, 7]], [[2, 1], [1, 6]], [[1, 2], [-1, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-2, 1], [-1, 6]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[1, -3]], [[1, 6]], [[1, -6]]]}
  • id: 6271156
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 10, 'counter': 56, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '48.15', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 5, 'label': '240.60.4a', 'nt': [24, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 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]], [[-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]], [[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: 6271157
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 10, 'counter': 57, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '240.60', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.60.4b1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, 1]], [[4, -1]], [[2, 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]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[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: 6271158
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 10, 'counter': 58, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '240.60', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.60.4b2', 'nt': [120, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, -1]], [[4, 1]], [[2, 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]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[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: 6271159
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 10, 'counter': 59, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '240.60', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.60.4b3', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -2]], [[4, 2]], [[2, 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]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[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: 6271161
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 10, 'counter': 60, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '240.60', 'group_counter': 60, 'group_order': 240, 'image': None, 'image_isoclass': '240.60', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.60.4b4', 'nt': [120, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 2]], [[4, -2]], [[2, 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]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[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]]]}
• 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: 64214300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 240, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '240.60.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '240.60', 'subgroup_hash': 60, 'subgroup_order': 240, 'subgroup_tex': 'C_{15}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64214311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 120, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': True, '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: 64214322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 120, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': '120.23', 'subgroup_hash': 23, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 64214333
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 120, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, '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': '120.1', 'subgroup_hash': 1, 'subgroup_order': 120, 'subgroup_tex': 'C_3:C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 64214339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 40, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '240.60.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '80.25', 'subgroup_hash': 25, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64214340
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 60, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 64214341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 30, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64214342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 30, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': True, 'core_order': 48, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '240.60.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64214301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 40, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, '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: 64214302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 20, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64214303
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 64214304
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 30, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['S', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64214305
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64214306
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 64214307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 24, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64214308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 24, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 64214309
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64214310
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 20, 'counter': 19, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 64214312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '240.60.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 2}
  • id: 64214315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 15, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '240.60.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 64214316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 12, 'counter': 24, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 64214317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64214318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 6, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 64214319
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 10, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214320
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.24.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214321
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64214323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.60.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64214324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64214325
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64214326
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 6, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64214327
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64214328
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 64214329
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 5, 'counter': 36, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '240.60.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.15', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_8', 'simple': True, 'solvable': True, 'special_labels': ['C5'], '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: 64214330
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 4, 'counter': 37, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64214331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64214332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.60.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64214334
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 3, 'counter': 40, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '240.60.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_8', 'simple': True, 'solvable': True, 'special_labels': ['L3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 64214335
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 2, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.60.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64214336
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64214337
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.60.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 64214338
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.60', 'ambient_counter': 60, 'ambient_order': 240, 'ambient_tex': 'C_{15}:D_8', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '240.60.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '240.60', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 60, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:D_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 64214312
    {'ambient': '240.60', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '60.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4454, -1, 4633, -1, 4419, -1, 8682, -1], 'generators': [1, 48, 8], 'label': '240.60.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214300
    {'ambient': '240.60', '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': '24.a1.a1', 'complements': ['240.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7891, 6656, 8220, 2489, 2892, 4287, 5235, 4287], 'generators': [1, 160, 48, 12, 2, 8], 'label': '240.60.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '24.8', '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': '24.8'}
  • id: 64214301
    {'ambient': '240.60', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.25', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': ['40.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7264, 6721, 7181, 6080, 2302, 9041, 8158, 9041], 'generators': [1, 48, 8, 12], 'label': '240.60.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '24.8', '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': '8.3'}
  • id: 64214302
    {'ambient': '240.60', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 12, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5486, -1, 5421, -1, 4980, -1, 3123, -1], 'generators': [3, 48, 8, 12], 'label': '240.60.6.b1.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.b1.a1', 'projective_image': '24.8', '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': '8.3'}
  • id: 64214303
    {'ambient': '240.60', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 24, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8537, -1, 8841, -1, 258, -1, 5522, -1], 'generators': [2, 4, 8, 48], 'label': '240.60.6.c1.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.c1.a1', 'projective_image': '24.8', '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': '2.1'}
  • id: 64214304
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3633, 2230, 3663, 8351, 6352, 3594, 3917, 3594], 'generators': [8, 48, 160], 'label': '240.60.8.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214305
    {'ambient': '240.60', 'aut_centralizer_order': 12, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '40.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1900, -1, 1682, -1, 7001, -1, 9714, -1], 'generators': [1, 48, 160], 'label': '240.60.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '48.15', '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': '1.1'}
  • id: 64214306
    {'ambient': '240.60', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '40.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [513, -1, 621, -1, 9569, -1, 479, -1], 'generators': [3, 160, 48], 'label': '240.60.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '48.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 64214307
    {'ambient': '240.60', 'aut_centralizer_order': 24, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '8.a1.a1', 'complements': ['24.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '30.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8262, 9564, 8339, 2363, 3312, 6833, 7037, 6833], 'generators': [1, 12, 160, 8], 'label': '240.60.10.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', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '120.25', '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': '8.3'}
  • id: 64214308
    {'ambient': '240.60', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': ['24.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '30.b1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5856, 5009, 7012, 4121, 5813, 2095, 2198, 2095], 'generators': [3, 12, 8, 160], 'label': '240.60.10.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'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '120.25', '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': '24.8'}
  • id: 64214309
    {'ambient': '240.60', 'aut_centralizer_order': 16, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': ['24.b1.a1', '24.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.c1.a1'], 'core': '10.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9818, 7092, 9811, 575, 922, 3562, 4785, 3562], 'generators': [2, 4, 8, 160], 'label': '240.60.10.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.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '120.25', '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': '12.4'}
  • id: 64214310
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 3878, 6043, 6873, 2309, 6430, 5358, 6430], 'generators': [12, 8, 48], 'label': '240.60.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214311
    {'ambient': '240.60', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.196', 'aut_weyl_index': 6, 'centralizer': '8.a1.a1', 'complements': ['120.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7015, 7998, 7341, 3779, 3836, 8010, 7413, 8010], 'generators': [1, 160, 48, 12, 8], 'label': '240.60.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '24.8', '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': '8.3'}
  • id: 64214313
    {'ambient': '240.60', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '60.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2837, -1, 2519, -1, 7931, -1, 2296, -1], 'generators': [3, 48, 8], 'label': '240.60.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '24.8', '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': '2.1'}
  • id: 64214314
    {'ambient': '240.60', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8915, -1, 9280, -1, 1527, -1, 6177, -1], 'generators': [1, 2], 'label': '240.60.15.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': '120.25', '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': '8.3'}
  • id: 64214315
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['48.a1.a1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1004, 1114, 1019, 9425, 7953, 3078, 3803, 3078], 'generators': [160, 48], 'label': '240.60.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214316
    {'ambient': '240.60', 'aut_centralizer_order': 96, 'aut_label': '20.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '60.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6604, 5865, 7368, 4044, 2958, 5012, 4638, 5012], 'generators': [12, 160, 8], 'label': '240.60.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '120.25', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64214317
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '60.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5337, -1, 5345, -1, 5526, -1, 7454, -1], 'generators': [1, 8, 160], 'label': '240.60.20.b1.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.b1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214318
    {'ambient': '240.60', 'aut_centralizer_order': 16, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.b1.a1'], 'contains': ['40.a1.a1', '40.c1.a1', '60.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2844, -1, 3294, -1, 8801, -1, 1330, -1], 'generators': [3, 8, 160], 'label': '240.60.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 64214319
    {'ambient': '240.60', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3814, 2343, 4194, 8056, 4987, 5657, 5113, 5657], 'generators': [8, 48], 'label': '240.60.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64214320
    {'ambient': '240.60', 'aut_centralizer_order': 24, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 96, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.a1.a1', '120.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1685, -1, 1542, -1, 6168, -1, 8396, -1], 'generators': [1, 48], 'label': '240.60.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '48.15', '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': '1.1'}
  • id: 64214321
    {'ambient': '240.60', 'aut_centralizer_order': 8, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 96, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '120.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [452, -1, 663, -1, 8602, -1, 2296, -1], 'generators': [3, 48], 'label': '240.60.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.c1.a1', 'projective_image': '48.15', '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': '1.1'}
  • id: 64214322
    {'ambient': '240.60', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 2, 'centralizer': '24.a1.a1', 'complements': ['120.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '6.b1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5910, 2633, 6014, 6329, 5046, 1176, 2812, 1176], 'generators': [3, 48, 8, 12, 160], 'label': '240.60.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '24.8', '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': '24.8'}
  • id: 64214323
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 48, 'centralizer': '8.a1.a1', 'complements': ['8.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7655, 8142, 8136, 5039, 1719, 7720, 6602, 7720], 'generators': [1, 12], 'label': '240.60.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '120.25', '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': '8.3'}
  • id: 64214324
    {'ambient': '240.60', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 48, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6179, -1, 6335, -1, 3549, -1, 3262, -1], 'generators': [3, 12], 'label': '240.60.30.b1.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.b1.a1', 'projective_image': '120.25', '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': '8.3'}
  • id: 64214325
    {'ambient': '240.60', 'aut_centralizer_order': 32, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9232, -1, 9531, -1, 1062, -1, 6013, -1], 'generators': [2], 'label': '240.60.30.c1.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.c1.a1', 'projective_image': '120.25', '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': '2.1'}
  • id: 64214326
    {'ambient': '240.60', 'aut_centralizer_order': 192, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4353, 3442, 3734, 6873, 5577, 4367, 4458, 4367], 'generators': [8, 160], 'label': '240.60.40.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '120.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214327
    {'ambient': '240.60', 'aut_centralizer_order': 48, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '120.b1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3424, -1, 2547, -1, 6758, -1, 7454, -1], 'generators': [1, 160], 'label': '240.60.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.60', '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': '1.1'}
  • id: 64214328
    {'ambient': '240.60', 'aut_centralizer_order': 16, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '120.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1429, -1, 189, -1, 9193, -1, 1486, -1], 'generators': [3, 160], 'label': '240.60.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '40.c1.a1', 'projective_image': '240.60', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 64214329
    {'ambient': '240.60', 'aut_centralizer_order': 96, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [182, 436, 1368, 9299, 6699, 4496, 4523, 4496], 'generators': [48], 'label': '240.60.48.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'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.15', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64214330
    {'ambient': '240.60', 'aut_centralizer_order': 192, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7028, 4846, 7277, 5551, 2634, 6946, 5768, 6946], 'generators': [12], 'label': '240.60.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '120.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214331
    {'ambient': '240.60', 'aut_centralizer_order': 96, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4750, -1, 5421, -1, 4360, -1, 6823, -1], 'generators': [1, 8], 'label': '240.60.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214332
    {'ambient': '240.60', 'aut_centralizer_order': 32, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.b1.a1'], 'contains': ['120.a1.a1', '120.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3059, -1, 3224, -1, 7326, -1, 2992, -1], 'generators': [3, 8], 'label': '240.60.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '120.25', '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': '2.1'}
  • id: 64214333
    {'ambient': '240.60', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.206', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': ['120.b1.a1', '120.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8579, 5315, 8932, 1198, 922, 5334, 4171, 5334], 'generators': [2, 4, 8, 48, 160], 'label': '240.60.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '24.8', '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': '12.4'}
  • id: 64214334
    {'ambient': '240.60', 'aut_centralizer_order': 192, 'aut_label': '80.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'contains': ['240.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1482, 1567, 1081, 8134, 7230, 3336, 3934, 3336], 'generators': [160], 'label': '240.60.80.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.60', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214335
    {'ambient': '240.60', 'aut_centralizer_order': 384, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1'], 'contains': ['240.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4151, 2940, 3971, 7247, 5282, 5657, 5113, 5657], 'generators': [8], 'label': '240.60.120.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.25', 'quotient_action_image': '1.1', 'quotient_action_kernel': '120.25', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64214336
    {'ambient': '240.60', 'aut_centralizer_order': 96, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.b1.a1', '60.b1.a1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2783, -1, 2296, -1, 6168, -1, 7135, -1], 'generators': [1], 'label': '240.60.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '120.b1.a1', 'projective_image': '240.60', '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': '1.1'}
  • id: 64214337
    {'ambient': '240.60', 'aut_centralizer_order': 32, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.c1.a1', '60.c1.a1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1058, -1, 488, -1, 8182, -1, 2648, -1], 'generators': [3], 'label': '240.60.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.60', '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': '1.1'}
  • id: 64214338
    {'ambient': '240.60', 'aut_centralizer_order': None, 'aut_label': '240.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': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.c1.a1'], 'contains': [], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1482, 1567, 1466, 8134, 6699, 4496, 4523, 4496], 'generators': [], 'label': '240.60.240.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': [], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.60', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64214339
    {'ambient': '240.60', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 6, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7952, -1, 8220, -1, 2044, -1, 6177, -1], 'generators': [1, 48, 12, 2, 8], 'label': '240.60.3.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': '24.8', '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': '8.3'}
  • id: 64214340
    {'ambient': '240.60', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 24, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6502, 4168, 6510, 6314, 4146, 5012, 4048, 5012], 'generators': [12, 48, 8, 160], 'label': '240.60.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64214341
    {'ambient': '240.60', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 24, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '12.b1.a1', '20.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4366, -1, 4543, -1, 6743, -1, 9386, -1], 'generators': [1, 160, 48, 8], 'label': '240.60.4.b1.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.b1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64214342
    {'ambient': '240.60', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.c1.a1', '20.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2837, -1, 3133, -1, 7945, -1, 1167, -1], 'generators': [3, 48, 160, 8], 'label': '240.60.4.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.c1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 64214343
    {'ambient': '240.60', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': ['48.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9265, 8854, 9811, 1991, 2892, 3239, 5235, 3239], 'generators': [1, 160, 2, 12, 8], 'label': '240.60.5.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.b1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '120.25', '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': '24.8'}