Abstract group data - 480.1021

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 4, 12, 2, 2], 'aut_gens': [[1, 2, 12, 24], [129, 370, 252, 276], [247, 242, 12, 24], [1, 2, 12, 312], [363, 374, 372, 156], [373, 254, 252, 24], [133, 374, 12, 264]], 'aut_group': '768.1088688', 'aut_hash': 1088688, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 768, 'aut_permdeg': 28, 'aut_perms': [77973651842526452938289607208, 57913094151882717304783836964, 1466521589953350870, 148095838912956297269708296132, 81510259129765109070459719464, 5399248879312863264326506713], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 2, 1], [3, 8, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [5, 1, 4, 1], [6, 8, 1, 1], [8, 12, 2, 1], [10, 1, 4, 1], [10, 6, 4, 1], [10, 12, 8, 1], [12, 8, 2, 1], [15, 8, 4, 1], [20, 2, 4, 1], [20, 6, 4, 1], [30, 8, 4, 1], [40, 12, 8, 1], [60, 8, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times D_4\\times S_4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.48', 'autcentquo_hash': 48, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 12, 2], [3, 8, 1], [4, 2, 1], [4, 6, 1], [5, 1, 4], [6, 8, 1], [8, 12, 2], [10, 1, 4], [10, 6, 4], [10, 12, 8], [12, 8, 2], [15, 8, 4], [20, 2, 4], [20, 6, 4], [30, 8, 4], [40, 12, 8], [60, 8, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '48.48', 'commutator_count': 1, 'commutator_label': '24.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1021, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['96.193', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 1, 2], [3, 8, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [5, 1, 4, 1], [6, 8, 1, 1], [8, 12, 1, 2], [10, 1, 4, 1], [10, 6, 4, 1], [10, 12, 4, 2], [12, 8, 2, 1], [15, 8, 4, 1], [20, 2, 4, 1], [20, 6, 4, 1], [30, 8, 4, 1], [40, 12, 4, 2], [60, 8, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 54, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.196', 'hash': 1021, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 2, 2], 'inner_gens': [[1, 250, 120, 396], [5, 2, 360, 276], [133, 374, 12, 264], [373, 254, 252, 24]], 'inner_hash': 48, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'C_2\\times S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 20], [2, 10], [3, 20], [4, 15]], 'label': '480.1021', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 24, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'GL(2,3):C10', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 65, 'number_divisions': 24, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 64, 'number_subgroup_classes': 84, 'number_subgroups': 346, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 8], [4, 8], [5, 4], [6, 8], [8, 24], [10, 124], [12, 16], [15, 32], [20, 32], [30, 32], [40, 96], [60, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [6, 0, 0], 'outer_gens': [[7, 2, 12, 24], [1, 10, 120, 396], [1, 2, 12, 312]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [120, 5040, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4], [4, 5], [8, 3], [12, 4], [16, 1], [32, 1]], 'representations': {'PC': {'code': 1117766232011583064909021941496115488139994169603, 'gens': [1, 2, 4, 5], 'pres': [7, -2, -2, -3, -2, 2, -2, -5, 3501, 36, 5210, 1276, 3363, 5050, 941, 584, 13864, 4841, 1383, 795, 102, 124]}, 'Perm': {'d': 21, 'gens': [499762408958628480, 2824932686085861840, 33, 40593484126995120, 5496238066015801440, 8074576096790193360, 10271542109627555280]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\GL(2,3):C_{10}', 'transitive_degree': 80, '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: 110383387
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1021, 'group_order': 480, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 110383398
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1021, 'group_order': 480, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 240, 'size': 1}
  • id: 110383409
    {'aut_label': '2B', 'centralizer': '6.b1.a1', 'counter': 3, 'group_counter': 1021, 'group_order': 480, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 126, 'size': 6}
  • id: 110383420
    {'aut_label': '2C', 'centralizer': '12.b1.a1', 'counter': 4, 'group_counter': 1021, 'group_order': 480, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1, 'size': 12}
  • id: 110383431
    {'aut_label': '2C', 'centralizer': '12.b1.a1', 'counter': 5, 'group_counter': 1021, 'group_order': 480, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 3, 'size': 12}
  • id: 110383442
    {'aut_label': '3A', 'centralizer': '8.b1.a1', 'counter': 6, 'group_counter': 1021, 'group_order': 480, 'label': '3A', 'order': 3, 'powers': [6, 1, 6], 'representative': 244, 'size': 8}
  • id: 110383449
    {'aut_label': '4A', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 1021, 'group_order': 480, 'label': '4A', 'order': 4, 'powers': [2, 7, 7], 'representative': 6, 'size': 2}
  • id: 110383450
    {'aut_label': '4B', 'centralizer': '6.c1.a1', 'counter': 8, 'group_counter': 1021, 'group_order': 480, 'label': '4B', 'order': 4, 'powers': [2, 8, 8], 'representative': 132, 'size': 6}
  • id: 110383451
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 1021, 'group_order': 480, 'label': '5A1', 'order': 5, 'powers': [11, 12, 1], 'representative': 288, 'size': 1}
  • id: 110383388
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 1021, 'group_order': 480, 'label': '5A-1', 'order': 5, 'powers': [12, 11, 1], 'representative': 192, 'size': 1}
  • id: 110383389
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 1021, 'group_order': 480, 'label': '5A2', 'order': 5, 'powers': [10, 9, 1], 'representative': 96, 'size': 1}
  • id: 110383390
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 1021, 'group_order': 480, 'label': '5A-2', 'order': 5, 'powers': [9, 10, 1], 'representative': 384, 'size': 1}
  • id: 110383391
    {'aut_label': '6A', 'centralizer': '8.b1.a1', 'counter': 13, 'group_counter': 1021, 'group_order': 480, 'label': '6A', 'order': 6, 'powers': [6, 2, 13], 'representative': 248, 'size': 8}
  • id: 110383392
    {'aut_label': '8A', 'centralizer': '12.g1.a1', 'counter': 14, 'group_counter': 1021, 'group_order': 480, 'label': '8A', 'order': 8, 'powers': [8, 14, 14], 'representative': 361, 'size': 12}
  • id: 110383393
    {'aut_label': '8A', 'centralizer': '12.g1.b1', 'counter': 15, 'group_counter': 1021, 'group_order': 480, 'label': '8B', 'order': 8, 'powers': [8, 15, 15], 'representative': 255, 'size': 12}
  • id: 110383394
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 1021, 'group_order': 480, 'label': '10A1', 'order': 10, 'powers': [10, 18, 2], 'representative': 336, 'size': 1}
  • id: 110383395
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 1021, 'group_order': 480, 'label': '10A-1', 'order': 10, 'powers': [9, 19, 2], 'representative': 144, 'size': 1}
  • id: 110383396
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 1021, 'group_order': 480, 'label': '10A3', 'order': 10, 'powers': [11, 17, 2], 'representative': 48, 'size': 1}
  • id: 110383397
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 1021, 'group_order': 480, 'label': '10A-3', 'order': 10, 'powers': [12, 16, 2], 'representative': 432, 'size': 1}
  • id: 110383399
    {'aut_label': '10B1', 'centralizer': '6.b1.a1', 'counter': 20, 'group_counter': 1021, 'group_order': 480, 'label': '10B1', 'order': 10, 'powers': [9, 22, 3], 'representative': 30, 'size': 6}
  • id: 110383400
    {'aut_label': '10B1', 'centralizer': '6.b1.a1', 'counter': 21, 'group_counter': 1021, 'group_order': 480, 'label': '10B-1', 'order': 10, 'powers': [10, 23, 3], 'representative': 114, 'size': 6}
  • id: 110383401
    {'aut_label': '10B1', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 1021, 'group_order': 480, 'label': '10B3', 'order': 10, 'powers': [12, 21, 3], 'representative': 78, 'size': 6}
  • id: 110383402
    {'aut_label': '10B1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 1021, 'group_order': 480, 'label': '10B-3', 'order': 10, 'powers': [11, 20, 3], 'representative': 66, 'size': 6}
  • id: 110383403
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 24, 'group_counter': 1021, 'group_order': 480, 'label': '10C1', 'order': 10, 'powers': [10, 26, 4], 'representative': 97, 'size': 12}
  • id: 110383404
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 25, 'group_counter': 1021, 'group_order': 480, 'label': '10C-1', 'order': 10, 'powers': [9, 27, 4], 'representative': 385, 'size': 12}
  • id: 110383405
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 26, 'group_counter': 1021, 'group_order': 480, 'label': '10C3', 'order': 10, 'powers': [11, 25, 4], 'representative': 49, 'size': 12}
  • id: 110383406
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 27, 'group_counter': 1021, 'group_order': 480, 'label': '10C-3', 'order': 10, 'powers': [12, 24, 4], 'representative': 193, 'size': 12}
  • id: 110383407
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 28, 'group_counter': 1021, 'group_order': 480, 'label': '10D1', 'order': 10, 'powers': [10, 30, 5], 'representative': 99, 'size': 12}
  • id: 110383408
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 29, 'group_counter': 1021, 'group_order': 480, 'label': '10D-1', 'order': 10, 'powers': [9, 31, 5], 'representative': 27, 'size': 12}
  • id: 110383410
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 30, 'group_counter': 1021, 'group_order': 480, 'label': '10D3', 'order': 10, 'powers': [11, 29, 5], 'representative': 51, 'size': 12}
  • id: 110383411
    {'aut_label': '10C1', 'centralizer': '12.b1.a1', 'counter': 31, 'group_counter': 1021, 'group_order': 480, 'label': '10D-3', 'order': 10, 'powers': [12, 28, 5], 'representative': 195, 'size': 12}
  • id: 110383412
    {'aut_label': '12A1', 'centralizer': '8.b1.a1', 'counter': 32, 'group_counter': 1021, 'group_order': 480, 'label': '12A1', 'order': 12, 'powers': [13, 7, 33], 'representative': 10, 'size': 8}
  • id: 110383413
    {'aut_label': '12A1', 'centralizer': '8.b1.a1', 'counter': 33, 'group_counter': 1021, 'group_order': 480, 'label': '12A5', 'order': 12, 'powers': [13, 7, 32], 'representative': 2, 'size': 8}
  • id: 110383414
    {'aut_label': '15A1', 'centralizer': '8.b1.a1', 'counter': 34, 'group_counter': 1021, 'group_order': 480, 'label': '15A1', 'order': 15, 'powers': [36, 10, 6], 'representative': 392, 'size': 8}
  • id: 110383415
    {'aut_label': '15A1', 'centralizer': '8.b1.a1', 'counter': 35, 'group_counter': 1021, 'group_order': 480, 'label': '15A-1', 'order': 15, 'powers': [37, 9, 6], 'representative': 340, 'size': 8}
  • id: 110383416
    {'aut_label': '15A1', 'centralizer': '8.b1.a1', 'counter': 36, 'group_counter': 1021, 'group_order': 480, 'label': '15A2', 'order': 15, 'powers': [35, 12, 6], 'representative': 52, 'size': 8}
  • id: 110383417
    {'aut_label': '15A1', 'centralizer': '8.b1.a1', 'counter': 37, 'group_counter': 1021, 'group_order': 480, 'label': '15A-2', 'order': 15, 'powers': [34, 11, 6], 'representative': 200, 'size': 8}
  • id: 110383418
    {'aut_label': '20A1', 'centralizer': '2.a1.a1', 'counter': 38, 'group_counter': 1021, 'group_order': 480, 'label': '20A1', 'order': 20, 'powers': [16, 40, 7], 'representative': 294, 'size': 2}
  • id: 110383419
    {'aut_label': '20A1', 'centralizer': '2.a1.a1', 'counter': 39, 'group_counter': 1021, 'group_order': 480, 'label': '20A-1', 'order': 20, 'powers': [17, 41, 7], 'representative': 438, 'size': 2}
  • id: 110383421
    {'aut_label': '20A1', 'centralizer': '2.a1.a1', 'counter': 40, 'group_counter': 1021, 'group_order': 480, 'label': '20A3', 'order': 20, 'powers': [18, 39, 7], 'representative': 150, 'size': 2}
  • id: 110383422
    {'aut_label': '20A1', 'centralizer': '2.a1.a1', 'counter': 41, 'group_counter': 1021, 'group_order': 480, 'label': '20A-3', 'order': 20, 'powers': [19, 38, 7], 'representative': 102, 'size': 2}
  • id: 110383423
    {'aut_label': '20B1', 'centralizer': '6.c1.a1', 'counter': 42, 'group_counter': 1021, 'group_order': 480, 'label': '20B1', 'order': 20, 'powers': [16, 44, 8], 'representative': 420, 'size': 6}
  • id: 110383424
    {'aut_label': '20B1', 'centralizer': '6.c1.a1', 'counter': 43, 'group_counter': 1021, 'group_order': 480, 'label': '20B-1', 'order': 20, 'powers': [17, 45, 8], 'representative': 84, 'size': 6}
  • id: 110383425
    {'aut_label': '20B1', 'centralizer': '6.c1.a1', 'counter': 44, 'group_counter': 1021, 'group_order': 480, 'label': '20B3', 'order': 20, 'powers': [18, 43, 8], 'representative': 276, 'size': 6}
  • id: 110383426
    {'aut_label': '20B1', 'centralizer': '6.c1.a1', 'counter': 45, 'group_counter': 1021, 'group_order': 480, 'label': '20B-3', 'order': 20, 'powers': [19, 42, 8], 'representative': 228, 'size': 6}
  • id: 110383427
    {'aut_label': '30A1', 'centralizer': '8.b1.a1', 'counter': 46, 'group_counter': 1021, 'group_order': 480, 'label': '30A1', 'order': 30, 'powers': [34, 16, 13], 'representative': 196, 'size': 8}
  • id: 110383428
    {'aut_label': '30A1', 'centralizer': '8.b1.a1', 'counter': 47, 'group_counter': 1021, 'group_order': 480, 'label': '30A-1', 'order': 30, 'powers': [35, 17, 13], 'representative': 56, 'size': 8}
  • id: 110383429
    {'aut_label': '30A1', 'centralizer': '8.b1.a1', 'counter': 48, 'group_counter': 1021, 'group_order': 480, 'label': '30A7', 'order': 30, 'powers': [36, 19, 13], 'representative': 388, 'size': 8}
  • id: 110383430
    {'aut_label': '30A1', 'centralizer': '8.b1.a1', 'counter': 49, 'group_counter': 1021, 'group_order': 480, 'label': '30A-7', 'order': 30, 'powers': [37, 18, 13], 'representative': 344, 'size': 8}
  • id: 110383432
    {'aut_label': '40A1', 'centralizer': '12.g1.a1', 'counter': 50, 'group_counter': 1021, 'group_order': 480, 'label': '40A1', 'order': 40, 'powers': [42, 52, 14], 'representative': 25, 'size': 12}
  • id: 110383433
    {'aut_label': '40A1', 'centralizer': '12.g1.a1', 'counter': 51, 'group_counter': 1021, 'group_order': 480, 'label': '40A-1', 'order': 40, 'powers': [43, 53, 14], 'representative': 109, 'size': 12}
  • id: 110383434
    {'aut_label': '40A1', 'centralizer': '12.g1.a1', 'counter': 52, 'group_counter': 1021, 'group_order': 480, 'label': '40A3', 'order': 40, 'powers': [44, 51, 14], 'representative': 73, 'size': 12}
  • id: 110383435
    {'aut_label': '40A1', 'centralizer': '12.g1.a1', 'counter': 53, 'group_counter': 1021, 'group_order': 480, 'label': '40A-3', 'order': 40, 'powers': [45, 50, 14], 'representative': 61, 'size': 12}
  • id: 110383436
    {'aut_label': '40A1', 'centralizer': '12.g1.b1', 'counter': 54, 'group_counter': 1021, 'group_order': 480, 'label': '40B1', 'order': 40, 'powers': [43, 56, 15], 'representative': 111, 'size': 12}
  • id: 110383437
    {'aut_label': '40A1', 'centralizer': '12.g1.b1', 'counter': 55, 'group_counter': 1021, 'group_order': 480, 'label': '40B-1', 'order': 40, 'powers': [42, 57, 15], 'representative': 39, 'size': 12}
  • id: 110383438
    {'aut_label': '40A1', 'centralizer': '12.g1.b1', 'counter': 56, 'group_counter': 1021, 'group_order': 480, 'label': '40B3', 'order': 40, 'powers': [45, 55, 15], 'representative': 63, 'size': 12}
  • id: 110383439
    {'aut_label': '40A1', 'centralizer': '12.g1.b1', 'counter': 57, 'group_counter': 1021, 'group_order': 480, 'label': '40B-3', 'order': 40, 'powers': [44, 54, 15], 'representative': 207, 'size': 12}
  • id: 110383440
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 58, 'group_counter': 1021, 'group_order': 480, 'label': '60A1', 'order': 60, 'powers': [46, 38, 32], 'representative': 98, 'size': 8}
  • id: 110383441
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 59, 'group_counter': 1021, 'group_order': 480, 'label': '60A-1', 'order': 60, 'powers': [47, 39, 32], 'representative': 26, 'size': 8}
  • id: 110383443
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 60, 'group_counter': 1021, 'group_order': 480, 'label': '60A7', 'order': 60, 'powers': [48, 41, 33], 'representative': 74, 'size': 8}
  • id: 110383444
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 61, 'group_counter': 1021, 'group_order': 480, 'label': '60A-7', 'order': 60, 'powers': [49, 40, 33], 'representative': 50, 'size': 8}
  • id: 110383445
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 62, 'group_counter': 1021, 'group_order': 480, 'label': '60A13', 'order': 60, 'powers': [49, 40, 32], 'representative': 290, 'size': 8}
  • id: 110383446
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 63, 'group_counter': 1021, 'group_order': 480, 'label': '60A-13', 'order': 60, 'powers': [48, 41, 32], 'representative': 194, 'size': 8}
  • id: 110383447
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 64, 'group_counter': 1021, 'group_order': 480, 'label': '60A19', 'order': 60, 'powers': [47, 39, 33], 'representative': 146, 'size': 8}
  • id: 110383448
    {'aut_label': '60A1', 'centralizer': '8.b1.a1', 'counter': 65, 'group_counter': 1021, 'group_order': 480, 'label': '60A-19', 'order': 60, 'powers': [46, 38, 33], 'representative': 110, 'size': 8}
• 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: 4603347
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603358
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603364
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603365
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603370
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603348
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, -1, -2, 2, 2, 2, 2, 2, -1, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603351
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, 1, 1, 0, 3, -1, 3, 3, 3, 3, 0, -1, -1, 3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603352
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, 0, 3, -1, 3, 3, 3, 3, 0, 1, 1, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603353
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 1, -1, 1, 0, -3, -1, 3, 3, 3, 3, 0, 1, -1, 3, 3, 3, 3, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -1, -1, -1, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603354
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 1, 1, -1, 0, -3, -1, 3, 3, 3, 3, 0, -1, 1, 3, 3, 3, 3, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -1, -1, -1, -1, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603366
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1e', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603367
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1f', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -4, 4, -1, -1, -1, -1, 4, -4, 4, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603368
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1g', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, 4, -4, 4, -1, -1, -1, -1, 4, 4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603369
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, 4, 4, 4, -1, -1, -1, -1, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603360
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.4a', 'multiplicity': 1, 'nt': [24, 127], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, -2, 0, 0, 4, 4, 4, 4, 2, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603349
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.2c', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, -4, 8, 8, -2, -2, -2, -2, -4, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4603350
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.2d', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, -4, -8, 8, -2, -2, -2, -2, -4, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4603361
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.4b', 'multiplicity': 2, 'nt': [16, 190], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 2, 0, 0, 8, 8, 8, 8, -2, 0, 0, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603355
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3e', 'multiplicity': 4, 'nt': [20, 34], 'qdim': 12, 'qvalues': [12, 12, -4, 4, 4, 0, 12, -4, -3, -3, -3, -3, 0, -4, -4, -3, -3, -3, -3, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603356
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3f', 'multiplicity': 4, 'nt': [30, 34], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -4, 0, 12, -4, -3, -3, -3, -3, 0, 4, 4, -3, -3, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603357
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3g', 'multiplicity': 4, 'nt': [30, 65], 'qdim': 12, 'qvalues': [12, 12, 4, -4, 4, 0, -12, -4, -3, -3, -3, -3, 0, 4, -4, -3, -3, -3, -3, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603359
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.3h', 'multiplicity': 4, 'nt': [30, 65], 'qdim': 12, 'qvalues': [12, 12, 4, 4, -4, 0, -12, -4, -3, -3, -3, -3, 0, -4, 4, -3, -3, -3, -3, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603362
    {'cdim': 4, 'counter': 23, 'faithful': True, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.4c', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, 0, 0, -4, -4, -4, -4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4603363
    {'cdim': 4, 'counter': 24, 'faithful': True, 'group': '480.1021', 'group_order': 480, 'image': None, 'label': '480.1021.4d', 'multiplicity': 8, 'nt': [80, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 8, 0, 0, -8, -8, -8, -8, -8, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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: 7290846
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 480, 'label': '480.1021.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7290857
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 240, 'label': '480.1021.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7290868
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 240, 'label': '480.1021.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7290879
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 240, 'label': '480.1021.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7290890
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 96, 'label': '480.1021.1e1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]]]}
  • id: 7290901
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 96, 'label': '480.1021.1e2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]]]}
  • id: 7290908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 96, 'label': '480.1021.1e3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]]]}
  • id: 7290909
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 96, 'label': '480.1021.1e4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]]]}
  • id: 7290910
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 48, 'label': '480.1021.1f1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[-1, -1]], [[1, -1]], [[-1, 2]], [[1, 1]], [[-1, -2]], [[1, -2]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]]]}
  • id: 7290847
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 48, 'label': '480.1021.1f2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[-1, 1]], [[1, 1]], [[-1, -2]], [[1, -1]], [[-1, 2]], [[1, 2]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]]]}
  • id: 7290848
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 48, 'label': '480.1021.1f3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, -2]], [[-1, -1]], [[1, -1]], [[-1, -2]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]]]}
  • id: 7290849
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 48, 'label': '480.1021.1f4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -2]], [[1, -2]], [[-1, -1]], [[1, 2]], [[-1, 1]], [[1, 1]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]]]}
  • id: 7290850
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 48, 'label': '480.1021.1g1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[-1, -1]], [[1, 2]], [[-1, 1]], [[1, -2]], [[-1, -2]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]]]}
  • id: 7290851
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 48, 'label': '480.1021.1g2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[-1, 1]], [[1, -2]], [[-1, -1]], [[1, 2]], [[-1, 2]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]]]}
  • id: 7290852
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 48, 'label': '480.1021.1g3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, -2]], [[1, -1]], [[-1, -1]], [[1, -2]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]]]}
  • id: 7290853
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 48, 'label': '480.1021.1g4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[-1, -2]], [[1, -1]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]]]}
  • id: 7290854
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.1021.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]]]}
  • id: 7290855
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.1021.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]]]}
  • id: 7290856
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.1021.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]]]}
  • id: 7290858
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.1021.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]]]}
  • id: 7290859
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 80, 'label': '480.1021.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7290860
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 40, 'label': '480.1021.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7290861
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 23, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 16, 'label': '480.1021.2c1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]]]}
  • id: 7290862
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 24, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 16, 'label': '480.1021.2c2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]]]}
  • id: 7290863
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 25, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 16, 'label': '480.1021.2c3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]]]}
  • id: 7290864
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 26, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 16, 'label': '480.1021.2c4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]]]}
  • id: 7290865
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 27, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.1021.2d1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]]]}
  • id: 7290866
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 28, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.1021.2d2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]]]}
  • id: 7290867
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 29, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.1021.2d3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]]]}
  • id: 7290869
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 30, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.1021.2d4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]]]}
  • id: 7290870
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 20, 'label': '480.1021.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-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]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290871
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 20, 'label': '480.1021.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-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]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290872
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 10, 'label': '480.1021.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[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]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290873
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 10, 'label': '480.1021.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[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]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290874
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 35, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3e1', 'nt': [20, 34], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2]], [[3, -2]], [[3, 1]], [[3, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290875
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 36, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3e2', 'nt': [20, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -2]], [[3, 2]], [[3, -1]], [[3, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290876
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 37, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3e3', 'nt': [20, 34], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -2]], [[3, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290877
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 38, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3e4', 'nt': [20, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 2]], [[3, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290878
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 39, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3f1', 'nt': [30, 34], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2]], [[3, -2]], [[3, 1]], [[3, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290880
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 40, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3f2', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -2]], [[3, 2]], [[3, -1]], [[3, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290881
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 41, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3f3', 'nt': [30, 34], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -2]], [[3, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290882
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 42, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '120.37', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.1021.3f4', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 2]], [[3, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290883
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 43, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3g1', 'nt': [30, 65], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[-1, -1]], [[1, -1]], [[-1, 2]], [[1, 1]], [[-1, -2]], [[1, -2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2]], [[-3, -2]], [[-3, 1]], [[-3, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290884
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 44, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3g2', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[-1, 1]], [[1, 1]], [[-1, -2]], [[1, -1]], [[-1, 2]], [[1, 2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -2]], [[-3, 2]], [[-3, -1]], [[-3, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290885
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 45, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3g3', 'nt': [30, 65], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, -2]], [[-1, -1]], [[1, -1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, -2]], [[-3, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290886
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 46, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3g4', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -2]], [[1, -2]], [[-1, -1]], [[1, 2]], [[-1, 1]], [[1, 1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, 2]], [[-3, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290887
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 47, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3h1', 'nt': [30, 65], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[1, -1]], [[-1, -1]], [[1, 2]], [[-1, 1]], [[1, -2]], [[-1, -2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2]], [[-3, -2]], [[-3, 1]], [[-3, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290888
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 48, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3h2', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 2]], [[3, -2]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, -2]], [[3, 2]], [[3, 1]], [[3, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[1, 1]], [[-1, 1]], [[1, -2]], [[-1, -1]], [[1, 2]], [[-1, 2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -2]], [[-3, 2]], [[-3, -1]], [[-3, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290889
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 49, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3h3', 'nt': [30, 65], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, -2]], [[1, -1]], [[-1, -1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, -2]], [[-3, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290891
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 50, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '240.196', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.1021.3h4', 'nt': [30, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 2]], [[3, -2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -2]], [[3, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -2]], [[-1, -2]], [[1, -1]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, 2]], [[-3, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290892
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.1021.4a', 'nt': [24, 127], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290893
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 52, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.1021.4b1', 'nt': [16, 190], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]]]}
  • id: 7290894
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 53, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.1021.4b2', 'nt': [16, 190], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]]]}
  • id: 7290895
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 54, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4c1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -2]], [[4, 2]], [[4, 1]], [[4, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[-4, -2]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290896
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 55, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4c2', 'nt': [120, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 2]], [[4, -2]], [[4, -1]], [[4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, -2]], [[-4, 2]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290897
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 56, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4c3', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -2]], [[4, 2]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[-4, 2]], [[-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290898
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 57, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4c4', 'nt': [120, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 2]], [[4, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[-4, -2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7290899
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 58, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d1', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 6]], [[4, 24]], [[4, 12]], [[-4, 18]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 24]], [[4, 6]], [[4, 18]], [[-4, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 12]], [[-1, 18]], [[1, 24]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18]], [[-1, 12]], [[-1, 24]], [[1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 11]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [-1, 11]], [[1, 3], [-2, 13]], [[-1, 3], [2, 13]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]]]}
  • id: 7290900
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 59, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d2', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 24]], [[-4, 6]], [[-4, 18]], [[4, 12]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 6]], [[-4, 24]], [[-4, 12]], [[4, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 18]], [[1, 12]], [[-1, 6]], [[1, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 18]], [[1, 6]], [[-1, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[1, 3], [-2, 13]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[-1, 1], [-1, 11]], [[1, 1], [1, 11]], [[-1, 3], [2, 13]]]}
  • id: 7290902
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 60, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d3', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 6]], [[4, 24]], [[4, 12]], [[-4, 18]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 24]], [[4, 6]], [[4, 18]], [[-4, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 12]], [[-1, 18]], [[1, 24]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18]], [[-1, 12]], [[-1, 24]], [[1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 11]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [1, 11]], [[-1, 3], [2, 13]], [[1, 3], [-2, 13]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]]]}
  • id: 7290903
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 61, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d4', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 24]], [[-4, 6]], [[-4, 18]], [[4, 12]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 6]], [[-4, 24]], [[-4, 12]], [[4, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 18]], [[1, 12]], [[-1, 6]], [[1, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 18]], [[1, 6]], [[-1, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-1, 3], [2, 13]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[1, 1], [1, 11]], [[-1, 1], [-1, 11]], [[1, 3], [-2, 13]]]}
  • id: 7290904
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 62, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d5', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 18]], [[4, 12]], [[-4, 6]], [[4, 24]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 12]], [[4, 18]], [[-4, 24]], [[4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 6]], [[1, 24]], [[1, 12]], [[-1, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24]], [[1, 6]], [[-1, 12]], [[1, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 13]], [[-1, 1], [-1, 11]], [[1, 3], [-2, 13]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [1, 11]]]}
  • id: 7290905
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 63, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d6', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 12]], [[-4, 18]], [[4, 24]], [[-4, 6]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 18]], [[-4, 12]], [[4, 6]], [[-4, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 24]], [[-1, 6]], [[-1, 18]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[-1, 24]], [[1, 18]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [-1, 11]], [[1, 1], [1, 11]], [[1, 3], [-2, 13]], [[-1, 3], [2, 13]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]]]}
  • id: 7290906
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 64, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d7', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 18]], [[4, 12]], [[-4, 6]], [[4, 24]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 12]], [[4, 18]], [[-4, 24]], [[4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 6]], [[1, 24]], [[1, 12]], [[-1, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24]], [[1, 6]], [[-1, 12]], [[1, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 13]], [[1, 1], [1, 11]], [[-1, 3], [2, 13]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[-1, 1], [-1, 11]]]}
  • id: 7290907
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 65, 'cyclotomic_n': 60, 'dim': 4, 'faithful': True, 'field': [81, 0, 27, 0, 9, 0, 3, 0, 1], 'group': '480.1021', 'group_counter': 1021, 'group_order': 480, 'image': None, 'image_isoclass': '480.1021', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.1021.4d8', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 12]], [[-4, 18]], [[4, 24]], [[-4, 6]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 18]], [[-4, 12]], [[4, 6]], [[-4, 24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 24]], [[-1, 6]], [[-1, 18]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[-1, 24]], [[1, 18]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [2, 7], [1, 9], [1, 11], [-1, 15]], [[-2, 1], [2, 5], [2, 7], [1, 9], [-2, 13], [-2, 15]], [[1, 1], [1, 3], [-2, 7], [-1, 9], [-1, 11], [1, 15]], [[1, 1], [1, 11]], [[-1, 1], [-1, 11]], [[-1, 3], [2, 13]], [[1, 3], [-2, 13]], [[2, 1], [-2, 5], [-2, 7], [-1, 9], [2, 13], [2, 15]]]}
• 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: 66931876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 480, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '480.1021.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.1021', 'subgroup_hash': 1021, 'subgroup_order': 480, 'subgroup_tex': '\\GL(2,3):C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 66931887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 240, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.154', 'subgroup_hash': 154, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 66931898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 240, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.103', 'subgroup_hash': 103, 'subgroup_order': 240, 'subgroup_tex': 'C_5\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 240, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.103', 'subgroup_hash': 103, 'subgroup_order': 240, 'subgroup_tex': 'C_5\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 80, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '480.1021.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '160.197', 'subgroup_hash': 197, 'subgroup_order': 160, 'subgroup_tex': 'D_8:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 120, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.15', 'subgroup_hash': 15, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 20, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.23', 'subgroup_hash': 23, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66931953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': True, 'core_order': 96, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '480.1021.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.193', 'subgroup_hash': 193, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 66931959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 80, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.24', 'subgroup_hash': 24, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.25', 'subgroup_hash': 25, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.25', 'subgroup_hash': 25, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 40, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 40, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 20, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.8.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': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 66931886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 48, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 66931888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 48, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 48, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 40, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 66931893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931897
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 66931899
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 66931900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '480.1021.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 66931901
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 66931902
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 66931903
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 66931904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 24, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66931905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66931906
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 20, 'counter': 37, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.1021.24.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': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], '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: 66931907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.24.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.24.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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931911
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 66931912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.24.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a2', 'outer_equivalence': False, 'perfect': False, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66931915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66931922
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '480.1021.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 66931923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66931924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66931925
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.40.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66931926
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 10, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.1021.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U1', 'C4'], '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: 66931927
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 5, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931928
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931929
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66931930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.1021.60.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': ['D2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66931933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931938
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931939
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.60.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66931940
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': 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: 66931941
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': 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: 66931943
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.80.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': 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: 66931944
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 5, 'counter': 71, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '480.1021.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.193', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 193, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2', '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: 66931945
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 4, 'counter': 72, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.1021.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_5\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 66931946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66931947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 66931948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66931949
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66931950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66931951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.1021.120.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66931952
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '480.1021.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 66931954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 2, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.1021.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.196', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 196, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{10}\\times S_4', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'D3'], '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: 66931955
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 66931956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 66931957
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.1021.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 66931958
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.1021', 'ambient_counter': 1021, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '480.1021.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '480.1021', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1021, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D4', '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: 66931876
    {'ambient': '480.1021', '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': '48.a1.a1', 'complements': ['480.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '4.b1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7208, 9278, 3382, 7169, 3335, 5889, 2115, 4421], 'generators': [1, 120, 96, 244, 6, 240, 132], 'label': '480.1021.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '48.48', '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': '48.48'}
  • id: 66931877
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2161', 'aut_weyl_index': 6, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '30.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2942, -1, 5219, -1, 4771, -1, 8127, -1], 'generators': [1, 132, 96, 6, 240], 'label': '480.1021.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '48.48', '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: 66931878
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 12, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.g1.b1', '30.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4341, -1, 332, -1, 8943, -1, 6301, -1], 'generators': [121, 96, 132, 6, 240], 'label': '480.1021.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '48.48', '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': '8.5'}
  • id: 66931879
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.196', 'aut_weyl_index': 12, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.g1.b1', '30.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2213, -1, 2861, -1, 7458, -1, 7538, -1], 'generators': [1, 96, 372, 126, 240], 'label': '480.1021.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931880
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.196', 'aut_weyl_index': 12, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.b1', '12.g1.a1', '30.d1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2213, -1, 3683, -1, 7458, -1, 7004, -1], 'generators': [121, 96, 132, 126, 240], 'label': '480.1021.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931881
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.196', 'aut_weyl_index': 12, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '30.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5596, -1, 2277, -1, 5733, -1, 5439, -1], 'generators': [1, 96, 132, 120, 240], 'label': '480.1021.6.e1.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.e1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931882
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.196', 'aut_weyl_index': 12, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.b1', '12.g1.b1', '30.e1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5596, -1, 1181, -1, 5733, -1, 3925, -1], 'generators': [243, 96, 360, 252, 240], 'label': '480.1021.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931883
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.35', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '24.c1.a1', '40.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6224, -1, 7085, -1, 359, -1, 2388, -1], 'generators': [1, 96, 244, 240], 'label': '480.1021.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66931884
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.35', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '4.b1.a1'], 'contains': ['16.a1.a1', '16.b1.b1', '24.c1.b1', '40.a1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6224, -1, 7769, -1, 359, -1, 281, -1], 'generators': [243, 96, 244, 240], 'label': '480.1021.8.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66931885
    {'ambient': '480.1021', 'aut_centralizer_order': 12, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7623, -1, 5965, -1, 1171, -1, 1752, -1], 'generators': [6, 96, 240, 244], 'label': '480.1021.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '48.48', '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': '2.1'}
  • id: 66931886
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': ['48.c1.a1', '48.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.a1.a1', '40.b1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9650, 5960, 2362, 4551, 3908, 7169, 1541, 3914], 'generators': [6, 240, 244, 372, 120], 'label': '480.1021.10.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': '240.196', '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': '24.12'}
  • id: 66931887
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': ['240.c1.a1', '240.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '8.b1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8294, 4639, 4458, 1963, 3335, 2098, 1845, 8601], 'generators': [6, 240, 96, 252, 244, 120], 'label': '480.1021.2.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': '48.48', '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': '24.12'}
  • id: 66931888
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': ['48.b1.a1', '48.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.e1.a1', '40.a1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8724, 9135, 1337, 6870, 3395, 8905, 2731, 1495], 'generators': [1, 240, 244, 132, 120], 'label': '480.1021.10.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': '240.196', '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': '48.48'}
  • id: 66931889
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': ['48.b1.a1', '48.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.e1.b1', '40.a1.b1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8724, 9135, 2026, 8337, 3395, 8905, 176, 2609], 'generators': [243, 240, 244, 372, 120], 'label': '480.1021.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.b1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '240.196', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66931890
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.d1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7015, 2535, 2772, 3163, 4596, 3446, 4097, 6713], 'generators': [252, 96, 240, 120], 'label': '480.1021.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['48.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66931891
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.25', 'aut_weyl_index': 24, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.c1.b1', '24.e1.a1', '24.e1.a2', '60.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1064, -1, 6912, -1, 3793, -1, 9676, -1], 'generators': [1, 240, 96, 138], 'label': '480.1021.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '48.48', '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: 66931892
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '60.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2753, -1, 5104, -1, 6027, -1, 7394, -1], 'generators': [6, 96, 240, 252], 'label': '480.1021.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '48.48', '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': '4.2'}
  • id: 66931893
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 24, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.b1.a1', '24.d1.a1', '60.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3477, -1, 4041, -1, 7458, -1, 8514, -1], 'generators': [126, 96, 240, 252], 'label': '480.1021.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931894
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.25', 'aut_weyl_index': 24, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '60.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4139, -1, 6093, -1, 2562, -1, 6274, -1], 'generators': [1, 96, 240, 6], 'label': '480.1021.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931895
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.25', 'aut_weyl_index': 24, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '60.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1841, -1, 3594, -1, 5279, -1, 9048, -1], 'generators': [1, 96, 240, 132], 'label': '480.1021.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931896
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.25', 'aut_weyl_index': 24, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.c1.b1', '24.d1.a1', '60.f1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1841, -1, 4615, -1, 5279, -1, 7979, -1], 'generators': [243, 96, 240, 120], 'label': '480.1021.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931897
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.d1.a1', '60.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4684, -1, 1366, -1, 8968, -1, 5490, -1], 'generators': [121, 132, 240, 96], 'label': '480.1021.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931898
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 4, 'centralizer': '48.a1.a1', 'complements': ['240.b1.a1', '240.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.e1.a1', '8.a1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7208, 9278, 3040, 5512, 2213, 5889, 2872, 3091], 'generators': [1, 240, 244, 132, 96, 120], 'label': '480.1021.2.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': '48.48', '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': '48.48'}
  • id: 66931899
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '12.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.e1.b1'], 'contains': ['24.d1.a1', '60.g1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4684, -1, 682, -1, 8968, -1, 5833, -1], 'generators': [15, 360, 240, 96], 'label': '480.1021.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931900
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.226', 'aut_weyl_index': 12, 'centralizer': '48.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', '30.d1.a1', '30.d1.b1', '30.e1.a1', '30.e1.b1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5606, -1, 1220, -1, 8081, -1, 3274, -1], 'generators': [1, 6, 120], 'label': '480.1021.15.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': '240.196', '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': '16.11'}
  • id: 66931901
    {'ambient': '480.1021', 'aut_centralizer_order': 24, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1', '8.a1.b1', '8.b1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '80.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7401, -1, 7835, -1, 942, -1, 1752, -1], 'generators': [240, 96, 244], 'label': '480.1021.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931902
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.5', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '80.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6026, -1, 9262, -1, 384, -1, 2813, -1], 'generators': [1, 244, 96], 'label': '480.1021.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66931903
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.5', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1'], 'contains': ['32.a1.a1', '48.c1.b1', '80.b1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6026, -1, 9703, -1, 384, -1, 1315, -1], 'generators': [243, 244, 96], 'label': '480.1021.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '16.b1.b1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66931904
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '20.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': ['24.e1.a1', '24.e1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['60.a1.a1', '80.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9274, 7403, 2479, 5781, 3121, 7018, 913, 3914], 'generators': [244, 372, 120, 240], 'label': '480.1021.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.b1', '10.b1.a1'], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '240.196', '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': '24.12'}
  • id: 66931905
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '5.a1.a1'], 'contains': ['40.a1.a1', '40.a1.b1', '40.b1.a1', '60.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8666, -1, 4899, -1, 1615, -1, 1405, -1], 'generators': [1, 6, 240, 244], 'label': '480.1021.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '240.196', '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': '12.4'}
  • id: 66931945
    {'ambient': '480.1021', 'aut_centralizer_order': 384, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.b1.a1', '60.c1.a1', '60.e1.a1'], 'contains': ['240.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5606, 969, 4488, 3147, 3789, 4170, 4397, 6169], 'generators': [6], 'label': '480.1021.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '30.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '240.196', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.9', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931906
    {'ambient': '480.1021', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4070, 722, 5555, 1286, 3185, 1542, 4397, 8145], 'generators': [6, 240, 96], 'label': '480.1021.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '48.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931907
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '120.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2479, -1, 6090, -1, 4985, -1, 8201, -1], 'generators': [258, 96, 240], 'label': '480.1021.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '48.48', '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': '2.1'}
  • id: 66931908
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '120.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1691, -1, 7528, -1, 2557, -1, 7242, -1], 'generators': [1, 96, 240], 'label': '480.1021.24.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '48.48', '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': '2.1'}
  • id: 66931909
    {'ambient': '480.1021', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 4, 'centralizer': '48.a1.a1', 'complements': ['240.b1.a1', '240.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.e1.b1', '8.a1.b1', '10.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7208, 9278, 3725, 8825, 2213, 5889, 390, 5751], 'generators': [243, 240, 244, 372, 96, 120], 'label': '480.1021.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '48.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66931910
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.b1.a1', '12.e1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '48.c1.b1', '120.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1691, -1, 6996, -1, 2557, -1, 6606, -1], 'generators': [243, 96, 240], 'label': '480.1021.24.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.c1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931911
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.a1.a1', '120.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3637, -1, 4152, -1, 6381, -1, 6114, -1], 'generators': [252, 240, 96], 'label': '480.1021.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931912
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.c1.b1', '120.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [350, -1, 8718, -1, 4172, -1, 8837, -1], 'generators': [1, 96, 138], 'label': '480.1021.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931913
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.c1.b1', '120.e1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [350, -1, 8186, -1, 4172, -1, 9473, -1], 'generators': [1, 96, 378], 'label': '480.1021.24.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.e1.a2', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931914
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': ['16.b1.a1', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.d1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7299, 4907, 1594, 3903, 8519, 5383, 3266, 5257], 'generators': [6, 252, 120], 'label': '480.1021.30.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', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '240.196', 'quotient_action_image': '6.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66931915
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 24, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.e1.a1', '60.f1.a1', '60.f1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4496, -1, 3823, -1, 6775, -1, 6808, -1], 'generators': [1, 6, 132], 'label': '480.1021.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '240.196', '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: 66931916
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.g1.a1', '60.g1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5804, -1, 251, -1, 9796, -1, 4561, -1], 'generators': [121, 6], 'label': '480.1021.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '240.196', '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': '8.5'}
  • id: 66931917
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '15.a1.a1'], 'contains': ['60.d1.a1', '60.f1.a1', '60.g1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3714, -1, 1862, -1, 9367, -1, 5178, -1], 'generators': [1, 126], 'label': '480.1021.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931918
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '15.a1.a1'], 'contains': ['60.d1.a1', '60.f1.b1', '60.g1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3714, -1, 2747, -1, 9367, -1, 4897, -1], 'generators': [121, 126], 'label': '480.1021.30.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.d1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931919
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.f1.a1', '60.g1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6649, -1, 750, -1, 8046, -1, 3636, -1], 'generators': [1, 120], 'label': '480.1021.30.e1.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.e1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931920
    {'ambient': '480.1021', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.27144', 'aut_weyl_index': 3, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4969, -1, 2636, -1, 6700, -1, 5439, -1], 'generators': [1, 240, 120, 96, 6, 132], 'label': '480.1021.3.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': '48.48', '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': '16.11'}
  • id: 66931921
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.f1.b1', '60.g1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6649, -1, 1096, -1, 8046, -1, 2895, -1], 'generators': [243, 252], 'label': '480.1021.30.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.e1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66931922
    {'ambient': '480.1021', 'aut_centralizer_order': 24, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['96.a1.a1', '160.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6586, -1, 9749, -1, 947, -1, 2431, -1], 'generators': [244, 96], 'label': '480.1021.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931923
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '10.b1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '120.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8482, -1, 5496, -1, 1341, -1, 2407, -1], 'generators': [1, 240, 244], 'label': '480.1021.40.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '40.a1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66931924
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '10.b1.b1', '20.b1.a1'], 'contains': ['80.a1.a1', '80.b1.b1', '120.c1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8482, -1, 6001, -1, 1341, -1, 761, -1], 'generators': [243, 240, 244], 'label': '480.1021.40.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '40.a1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66931925
    {'ambient': '480.1021', 'aut_centralizer_order': 48, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '10.a1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8907, -1, 4563, -1, 1740, -1, 2095, -1], 'generators': [6, 244, 240], 'label': '480.1021.40.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.196', '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': '2.1'}
  • id: 66931926
    {'ambient': '480.1021', 'aut_centralizer_order': 192, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1'], 'contains': ['96.a1.a1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2367, 1836, 6944, 1648, 2981, 2822, 6126, 7182], 'generators': [240, 96], 'label': '480.1021.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.48', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931927
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 192, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.e1.a1', '24.e1.a2'], 'contains': ['96.a1.a1', '240.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [659, -1, 7896, -1, 4188, -1, 8201, -1], 'generators': [258, 96], 'label': '480.1021.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931928
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 192, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.c1.a1', '24.e1.a1', '24.e1.a2'], 'contains': ['96.a1.a1', '240.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1084, -1, 8846, -1, 2542, -1, 7132, -1], 'generators': [1, 96], 'label': '480.1021.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931929
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 192, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.c1.b1', '24.e1.a1', '24.e1.a2'], 'contains': ['96.a1.a1', '240.c1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1084, -1, 8517, -1, 2542, -1, 6789, -1], 'generators': [243, 96], 'label': '480.1021.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.c1.b1', 'projective_image': '96.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931930
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7440, 4639, 1530, 4724, 5982, 5383, 3242, 5257], 'generators': [252, 120], 'label': '480.1021.60.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': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66931931
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': ['120.e1.a1', '120.e1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['12.a1.a1', '16.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8357, 7217, 4110, 4913, 2463, 4423, 905, 5979], 'generators': [244, 252, 120, 96, 240], 'label': '480.1021.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '48.48', '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': '24.12'}
  • id: 66931932
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 96, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.b1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.c1.b1', '120.e1.a1', '120.e1.a2'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2358, -1, 6295, -1, 5598, -1, 7721, -1], 'generators': [1, 138, 240], 'label': '480.1021.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.b1.a1', 'projective_image': '240.196', '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: 66931933
    {'ambient': '480.1021', 'aut_centralizer_order': 64, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5973, -1, 3274, -1, 7298, -1, 4834, -1], 'generators': [6, 252], 'label': '480.1021.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '240.196', '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': '4.2'}
  • id: 66931934
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.a1.a1', '30.d1.a1', '30.d1.b1'], 'contains': ['120.b1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3222, -1, 2639, -1, 7817, -1, 5521, -1], 'generators': [126, 252], 'label': '480.1021.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931935
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.b1.a1', '30.b1.a1'], 'contains': ['120.a1.a1', '120.c1.a1', '120.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5471, -1, 4921, -1, 3584, -1, 4085, -1], 'generators': [1, 6], 'label': '480.1021.60.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.e1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931936
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.b1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.c1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3767, -1, 3614, -1, 6780, -1, 5802, -1], 'generators': [1, 132], 'label': '480.1021.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931937
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '30.b1.a1', '30.d1.b1', '30.e1.b1'], 'contains': ['120.c1.b1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3767, -1, 3856, -1, 6780, -1, 5240, -1], 'generators': [243, 120], 'label': '480.1021.60.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.f1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66931938
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '30.c1.a1', '30.d1.b1', '30.e1.a1'], 'contains': ['120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4939, -1, 724, -1, 8968, -1, 3523, -1], 'generators': [121], 'label': '480.1021.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931939
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '12.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '30.c1.a1', '30.d1.a1', '30.e1.b1'], 'contains': ['120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4939, -1, 352, -1, 8968, -1, 3804, -1], 'generators': [15], 'label': '480.1021.60.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.g1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66931940
    {'ambient': '480.1021', 'aut_centralizer_order': 96, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '20.a1.a1', '40.a1.a1', '40.a1.b1', '40.b1.a1'], 'contains': ['160.a1.a1', '240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8853, -1, 5659, -1, 1735, -1, 2095, -1], 'generators': [240, 244], 'label': '480.1021.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931941
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '40.a1.a1'], 'contains': ['160.a1.a1', '240.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7073, -1, 8634, -1, 1366, -1, 2790, -1], 'generators': [1, 244], 'label': '480.1021.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66931942
    {'ambient': '480.1021', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 4, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '12.e1.a1', '20.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6528, -1, 6161, -1, 1341, -1, 2240, -1], 'generators': [1, 96, 240, 6, 244], 'label': '480.1021.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '48.48', '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': '12.4'}
  • id: 66931943
    {'ambient': '480.1021', 'aut_centralizer_order': 8, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '40.a1.b1'], 'contains': ['160.a1.a1', '240.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7073, -1, 8868, -1, 1366, -1, 1565, -1], 'generators': [243, 244], 'label': '480.1021.80.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '80.b1.b1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66931944
    {'ambient': '480.1021', 'aut_centralizer_order': 192, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.c1.b1'], 'contains': ['480.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1209, 3237, 9276, 1411, 2832, 2890, 6805, 7157], 'generators': [96], 'label': '480.1021.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['48.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.193', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931946
    {'ambient': '480.1021', 'aut_centralizer_order': 128, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '60.b1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2396, -1, 5134, -1, 5314, -1, 6457, -1], 'generators': [258, 240], 'label': '480.1021.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '240.196', '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': '2.1'}
  • id: 66931947
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.a1.a1', '60.b1.a1', '60.e1.a1', '60.f1.a1'], 'contains': ['240.a1.a1', '240.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3405, -1, 5975, -1, 3405, -1, 5794, -1], 'generators': [1, 240], 'label': '480.1021.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.196', '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': '2.1'}
  • id: 66931948
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '40.a1.b1', '60.b1.a1', '60.e1.a1', '60.f1.b1'], 'contains': ['240.a1.a1', '240.c1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3405, -1, 6347, -1, 3405, -1, 5474, -1], 'generators': [243, 240], 'label': '480.1021.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.c1.b1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931949
    {'ambient': '480.1021', 'aut_centralizer_order': 128, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.a1.a1', '60.c1.a1', '60.d1.a1', '60.f1.a1', '60.f1.b1', '60.g1.a1', '60.g1.b1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4689, -1, 2990, -1, 6780, -1, 5174, -1], 'generators': [252], 'label': '480.1021.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '240.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931950
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.b1.a1'], 'contains': ['240.b1.a1', '240.c1.a1', '240.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1349, -1, 8010, -1, 4611, -1, 7464, -1], 'generators': [1, 138], 'label': '480.1021.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '120.e1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931951
    {'ambient': '480.1021', 'aut_centralizer_order': 16, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a2', '60.b1.a1'], 'contains': ['240.b1.a1', '240.c1.a1', '240.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1349, -1, 7619, -1, 4611, -1, 7784, -1], 'generators': [1, 378], 'label': '480.1021.120.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '120.e1.a2', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931952
    {'ambient': '480.1021', 'aut_centralizer_order': 96, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.a1.a1', '80.b1.a1', '80.b1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6890, -1, 9005, -1, 1550, -1, 2431, -1], 'generators': [244], 'label': '480.1021.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '160.a1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66931953
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 4, 'centralizer': '48.a1.a1', 'complements': ['96.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '15.a1.a1', '20.b1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9009, 9135, 1728, 8337, 4302, 8905, 1089, 823], 'generators': [1, 240, 120, 6, 244, 132], 'label': '480.1021.5.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.b1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '240.196', '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': '48.48'}
  • id: 66931954
    {'ambient': '480.1021', 'aut_centralizer_order': 768, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.c1.a1', '120.c1.b1', '120.d1.a1'], 'contains': ['480.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4689, 3073, 5480, 2847, 3549, 4136, 5634, 6219], 'generators': [240], 'label': '480.1021.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': -24, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '60.a1.a1', '120.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.196', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.196', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931955
    {'ambient': '480.1021', 'aut_centralizer_order': 128, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '120.b1.a1', '120.e1.a1', '120.e1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1402, -1, 7710, -1, 4397, -1, 7464, -1], 'generators': [258], 'label': '480.1021.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '240.b1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931956
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.b1.a1', '120.c1.a1', '120.e1.a1', '120.e1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1890, -1, 8144, -1, 3190, -1, 7101, -1], 'generators': [1], 'label': '480.1021.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '240.c1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931957
    {'ambient': '480.1021', 'aut_centralizer_order': 32, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '80.b1.b1', '120.c1.b1', '120.e1.a1', '120.e1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1890, -1, 8517, -1, 3190, -1, 6524, -1], 'generators': [243], 'label': '480.1021.240.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '240.c1.b1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931958
    {'ambient': '480.1021', 'aut_centralizer_order': None, 'aut_label': '480.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': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '240.c1.b1'], 'contains': [], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1890, 4124, 8330, 2263, 3190, 3496, 6664, 6675], 'generators': [], 'label': '480.1021.480.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['96.a1.a1', '240.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '480.1021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66931959
    {'ambient': '480.1021', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': ['80.b1.a1', '80.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6716, 1752, 4341, 1175, 6700, 1255, 4682, 8360], 'generators': [6, 120, 96, 252, 240], 'label': '480.1021.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '48.48', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}