Abstract group data - 480.970

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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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 2, 12, 10, 2], 'aut_gens': [[1, 2, 12, 24], [137, 130, 252, 276], [241, 2, 12, 24], [1, 242, 12, 24], [137, 134, 360, 420], [241, 62, 252, 24], [361, 134, 12, 264]], 'aut_group': '1920.240396', 'aut_hash': 3782145897709286038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 22, 'aut_perms': [413241976699165199670, 974025885318428741190, 9965653166037875926, 553557758144190792914, 6666266706311692107, 617240801136931061790], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 1, 1], [2, 30, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 6, 1, 1], [4, 10, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 12, 1, 1], [8, 60, 1, 1], [10, 2, 2, 1], [10, 24, 2, 1], [12, 40, 2, 1], [15, 16, 2, 1], [20, 12, 2, 1], [30, 16, 2, 1], [40, 12, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times F_5\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '480.1189', 'autcentquo_hash': 1189, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 12, 1], [2, 30, 1], [2, 60, 1], [3, 8, 1], [4, 6, 1], [4, 10, 1], [5, 2, 2], [6, 8, 1], [8, 12, 1], [8, 60, 1], [10, 2, 2], [10, 24, 2], [12, 40, 2], [15, 16, 2], [20, 12, 2], [30, 16, 2], [40, 12, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '240.194', 'commutator_count': 1, 'commutator_label': '120.15', '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': 970, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 1, 1], [2, 30, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 6, 1, 1], [4, 10, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 12, 1, 1], [8, 60, 1, 1], [10, 2, 2, 1], [10, 24, 2, 1], [12, 40, 2, 1], [15, 16, 2, 1], [20, 12, 2, 1], [30, 16, 2, 1], [40, 12, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 1, 4], [8, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.194', 'hash': 970, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 6, 2, 10], 'inner_gens': [[1, 250, 132, 264], [5, 2, 120, 468], [361, 134, 12, 264], [241, 62, 252, 24]], 'inner_hash': 194, 'inner_nilpotent': False, 'inner_order': 240, 'inner_split': True, 'inner_tex': 'D_5\\times S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 6], [3, 4], [4, 9], [6, 4], [8, 2]], 'label': '480.970', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'GL(2,3):D5', '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': 19, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 29, 'number_divisions': 19, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 82, 'number_subgroup_classes': 84, 'number_subgroups': 818, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 103], [3, 8], [4, 16], [5, 4], [6, 8], [8, 72], [10, 52], [12, 80], [15, 32], [20, 24], [30, 32], [40, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 10, 132, 264], [1, 2, 12, 312]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4], [4, 3], [8, 2], [12, 2], [16, 2]], 'representations': {'PC': {'code': 257003915320259386069650197707561524611449925924782339, 'gens': [1, 2, 4, 5], 'pres': [7, -2, -2, -3, -2, 2, -2, -5, 3501, 36, 5210, 1276, 3699, 1690, 2621, 584, 9244, 8201, 3483, 795, 102, 9084, 124, 9421]}, 'Perm': {'d': 21, 'gens': [2824932686085861847, 499762408958628480, 40593484126995120, 37, 5496238066015801440, 8074576096790193360, 10271542109627555280]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\GL(2,3):D_5', '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: 110419414
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 970, 'group_order': 480, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 110419425
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 970, 'group_order': 480, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 240, 'size': 1}
  • id: 110419436
    {'aut_label': '2B', 'centralizer': '12.b1.a1', 'counter': 3, 'group_counter': 970, 'group_order': 480, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 241, 'size': 12}
  • id: 110419437
    {'aut_label': '2C', 'centralizer': '30.a1.a1', 'counter': 4, 'group_counter': 970, 'group_order': 480, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 90, 'size': 30}
  • id: 110419438
    {'aut_label': '2D', 'centralizer': '60.b1.a1', 'counter': 5, 'group_counter': 970, 'group_order': 480, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 243, 'size': 60}
  • id: 110419439
    {'aut_label': '3A', 'centralizer': '8.c1.a1', 'counter': 6, 'group_counter': 970, 'group_order': 480, 'label': '3A', 'order': 3, 'powers': [6, 1, 6], 'representative': 244, 'size': 8}
  • id: 110419440
    {'aut_label': '4A', 'centralizer': '6.e1.a1', 'counter': 7, 'group_counter': 970, 'group_order': 480, 'label': '4A', 'order': 4, 'powers': [2, 7, 7], 'representative': 120, 'size': 6}
  • id: 110419441
    {'aut_label': '4B', 'centralizer': '10.b1.a1', 'counter': 8, 'group_counter': 970, 'group_order': 480, 'label': '4B', 'order': 4, 'powers': [2, 8, 8], 'representative': 198, 'size': 10}
  • id: 110419442
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 9, 'group_counter': 970, 'group_order': 480, 'label': '5A1', 'order': 5, 'powers': [10, 10, 1], 'representative': 96, 'size': 2}
  • id: 110419415
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 970, 'group_order': 480, 'label': '5A2', 'order': 5, 'powers': [9, 9, 1], 'representative': 192, 'size': 2}
  • id: 110419416
    {'aut_label': '6A', 'centralizer': '8.c1.a1', 'counter': 11, 'group_counter': 970, 'group_order': 480, 'label': '6A', 'order': 6, 'powers': [6, 2, 11], 'representative': 248, 'size': 8}
  • id: 110419417
    {'aut_label': '8A', 'centralizer': '12.h1.a1', 'counter': 12, 'group_counter': 970, 'group_order': 480, 'label': '8A', 'order': 8, 'powers': [7, 12, 12], 'representative': 253, 'size': 12}
  • id: 110419418
    {'aut_label': '8B', 'centralizer': '60.i1.a1', 'counter': 13, 'group_counter': 970, 'group_order': 480, 'label': '8B', 'order': 8, 'powers': [7, 13, 13], 'representative': 279, 'size': 60}
  • id: 110419419
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 970, 'group_order': 480, 'label': '10A1', 'order': 10, 'powers': [9, 15, 2], 'representative': 48, 'size': 2}
  • id: 110419420
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 970, 'group_order': 480, 'label': '10A3', 'order': 10, 'powers': [10, 14, 2], 'representative': 144, 'size': 2}
  • id: 110419421
    {'aut_label': '10B1', 'centralizer': '24.b1.a1', 'counter': 16, 'group_counter': 970, 'group_order': 480, 'label': '10B1', 'order': 10, 'powers': [9, 17, 3], 'representative': 49, 'size': 24}
  • id: 110419422
    {'aut_label': '10B1', 'centralizer': '24.b1.a1', 'counter': 17, 'group_counter': 970, 'group_order': 480, 'label': '10B3', 'order': 10, 'powers': [10, 16, 3], 'representative': 145, 'size': 24}
  • id: 110419423
    {'aut_label': '12A1', 'centralizer': '40.c1.a1', 'counter': 18, 'group_counter': 970, 'group_order': 480, 'label': '12A1', 'order': 12, 'powers': [11, 8, 19], 'representative': 194, 'size': 40}
  • id: 110419424
    {'aut_label': '12A1', 'centralizer': '40.c1.a1', 'counter': 19, 'group_counter': 970, 'group_order': 480, 'label': '12A5', 'order': 12, 'powers': [11, 8, 18], 'representative': 202, 'size': 40}
  • id: 110419426
    {'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 20, 'group_counter': 970, 'group_order': 480, 'label': '15A1', 'order': 15, 'powers': [21, 9, 6], 'representative': 200, 'size': 16}
  • id: 110419427
    {'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 21, 'group_counter': 970, 'group_order': 480, 'label': '15A2', 'order': 15, 'powers': [20, 10, 6], 'representative': 148, 'size': 16}
  • id: 110419428
    {'aut_label': '20A1', 'centralizer': '12.h1.a1', 'counter': 22, 'group_counter': 970, 'group_order': 480, 'label': '20A1', 'order': 20, 'powers': [15, 23, 7], 'representative': 312, 'size': 12}
  • id: 110419429
    {'aut_label': '20A1', 'centralizer': '12.h1.a1', 'counter': 23, 'group_counter': 970, 'group_order': 480, 'label': '20A3', 'order': 20, 'powers': [14, 22, 7], 'representative': 456, 'size': 12}
  • id: 110419430
    {'aut_label': '30A1', 'centralizer': '16.a1.a1', 'counter': 24, 'group_counter': 970, 'group_order': 480, 'label': '30A1', 'order': 30, 'powers': [20, 14, 11], 'representative': 100, 'size': 16}
  • id: 110419431
    {'aut_label': '30A1', 'centralizer': '16.a1.a1', 'counter': 25, 'group_counter': 970, 'group_order': 480, 'label': '30A7', 'order': 30, 'powers': [21, 15, 11], 'representative': 196, 'size': 16}
  • id: 110419432
    {'aut_label': '40A1', 'centralizer': '12.h1.a1', 'counter': 26, 'group_counter': 970, 'group_order': 480, 'label': '40A1', 'order': 40, 'powers': [22, 27, 12], 'representative': 109, 'size': 12}
  • id: 110419433
    {'aut_label': '40A1', 'centralizer': '12.h1.a1', 'counter': 27, 'group_counter': 970, 'group_order': 480, 'label': '40A3', 'order': 40, 'powers': [23, 28, 12], 'representative': 301, 'size': 12}
  • id: 110419434
    {'aut_label': '40A1', 'centralizer': '12.h1.a1', 'counter': 28, 'group_counter': 970, 'group_order': 480, 'label': '40A9', 'order': 40, 'powers': [22, 29, 12], 'representative': 37, 'size': 12}
  • id: 110419435
    {'aut_label': '40A1', 'centralizer': '12.h1.a1', 'counter': 29, 'group_counter': 970, 'group_order': 480, 'label': '40A13', 'order': 40, 'powers': [23, 26, 12], 'representative': 61, 'size': 12}
• 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: 4617306
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.1a', '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], 'schur_index': 1}
  • id: 4617317
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.1b', '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], 'schur_index': 1}
  • id: 4617318
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.1c', '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], 'schur_index': 1}
  • id: 4617319
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.1d', '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], 'schur_index': 1}
  • id: 4617320
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 0, -1, 2, 2, 2, 2, -1, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617321
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 0, -1, 2, -2, 2, 2, -1, 0, 0, 2, 2, 0, 0, 1, 1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617324
    {'cdim': 3, 'counter': 9, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 1, -1, 1, 0, -1, 3, 3, 3, 0, -1, -1, 3, 3, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4617307
    {'cdim': 3, 'counter': 10, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, 0, -1, 3, 3, 3, 0, 1, 1, 3, 3, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4617308
    {'cdim': 3, 'counter': 11, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, 1, 1, 0, -1, -3, 3, 3, 0, 1, -1, 3, 3, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4617309
    {'cdim': 3, 'counter': 12, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 1, 1, -1, 0, -1, -3, 3, 3, 0, -1, 1, 3, 3, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4617322
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.2c', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 4, 4, 0, -1, -1, 4, 4, 0, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4617323
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.2d', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 4, 4, 0, -1, -1, 4, -4, 0, -1, -1, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4617310
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.4a', 'multiplicity': 1, 'nt': [24, 127], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, -2, 0, 0, 4, 4, 2, 0, 0, -4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617311
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.4b', 'multiplicity': 2, 'nt': [15, 7], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, -4, 8, 0, -2, -2, -4, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617312
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.4c', 'multiplicity': 2, 'nt': [16, 190], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 2, 0, 0, 8, 8, -2, 0, 0, -8, -8, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617314
    {'cdim': 6, 'counter': 17, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.6a', 'multiplicity': 2, 'nt': [20, 69], 'qdim': 12, 'qvalues': [12, 12, 4, 0, 0, 0, -4, 0, -3, -3, 0, -4, 0, -3, -3, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4617315
    {'cdim': 6, 'counter': 18, 'faithful': False, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.6b', 'multiplicity': 2, 'nt': [30, 54], 'qdim': 12, 'qvalues': [12, 12, -4, 0, 0, 0, -4, 0, -3, -3, 0, 4, 0, -3, -3, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4617313
    {'cdim': 4, 'counter': 16, 'faithful': True, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.4d', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, 0, 0, -4, -4, 8, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4617316
    {'cdim': 8, 'counter': 19, 'faithful': True, 'group': '480.970', 'group_order': 480, 'image': None, 'label': '480.970.8a', 'multiplicity': 2, 'nt': [80, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 4, 0, 0, -4, -4, -4, 0, 0, 4, 4, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 2}
• 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: 7326873
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 480, 'label': '480.970.1a', '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]]]}
  • id: 7326884
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 240, 'label': '480.970.1b', '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]]]}
  • id: 7326895
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 240, 'label': '480.970.1c', '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]]]}
  • id: 7326896
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 240, 'label': '480.970.1d', '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]]]}
  • id: 7326897
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 80, 'label': '480.970.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326898
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 80, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 40, 'label': '480.970.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326899
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 48, 'counter': 7, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.970.2c1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 7326900
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 48, 'counter': 8, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 48, 'label': '480.970.2c2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 7326901
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 48, 'counter': 9, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 24, 'label': '480.970.2d1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 7326874
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 48, 'counter': 10, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 24, 'label': '480.970.2d2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 7326875
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 11, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 20, 'label': '480.970.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7326876
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 12, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 20, 'label': '480.970.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7326877
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 13, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 10, 'label': '480.970.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7326878
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 20, 'counter': 14, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 10, 'label': '480.970.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7326879
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.970.4a', '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]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326880
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.970.4b1', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -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]]]}
  • id: 7326881
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 8, 'label': '480.970.4b2', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -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]]]}
  • id: 7326882
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 18, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.970.4c1', '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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326883
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 10, 'counter': 19, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '96.193', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 5, 'label': '480.970.4c2', '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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326885
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [20, 0, -10, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.4d1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]]]}
  • id: 7326886
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [20, 0, -10, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.4d2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]]]}
  • id: 7326887
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [20, 0, -10, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.4d3', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]]]}
  • id: 7326888
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [20, 0, -10, 0, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.4d4', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]]]}
  • id: 7326889
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.970.6a1', 'nt': [20, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[-2, 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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 7326890
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.970.6a2', 'nt': [20, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[-2, 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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 7326891
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.970.6b1', 'nt': [30, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[2, 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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 7326892
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.970.6b2', 'nt': [30, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[2, 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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 7326893
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.8a1', 'nt': [80, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 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, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7326894
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '480.970', 'group_counter': 970, 'group_order': 480, 'image': None, 'image_isoclass': '480.970', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 1, 'label': '480.970.8a2', 'nt': [80, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 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, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 66982483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '480.970.1.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': '480.970', 'subgroup_hash': 970, 'subgroup_order': 480, 'subgroup_tex': '\\GL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 66982494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 240, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.2.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': ['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: 66982505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 66982516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.106', 'subgroup_hash': 106, 'subgroup_order': 240, 'subgroup_tex': 'C_5:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66982527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '480.970.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.135', 'subgroup_hash': 135, 'subgroup_order': 160, 'subgroup_tex': 'C_8:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 120, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.4.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': ['D', 'L1', 'D1', '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: 66982549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.4.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': '120.13', 'subgroup_hash': 13, 'subgroup_order': 120, 'subgroup_tex': 'C_5:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66982560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '480.970.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 66982566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 80, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66982484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66982485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.15', 'subgroup_hash': 15, 'subgroup_order': 80, 'subgroup_tex': 'C_5:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 40, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.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': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66982487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.5', 'subgroup_hash': 5, 'subgroup_order': 80, 'subgroup_tex': 'C_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66982488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.7', 'subgroup_hash': 7, 'subgroup_order': 80, 'subgroup_tex': 'D_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 66982489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.17', 'subgroup_hash': 17, 'subgroup_order': 80, 'subgroup_tex': 'Q_8:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66982490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.8.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: 66982491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 66982492
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 20, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66982493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 48, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.10.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': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', '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: 66982495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 66982496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66982497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 40, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.12.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': ['F', '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: 66982498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.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: 66982501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66982502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 66982503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 66982504
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 66982506
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '480.970.15.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: 66982508
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 10, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.16.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: 66982509
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.16.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: 66982510
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 66982511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 24, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.20.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': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 66982512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.20.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: 66982513
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 20, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.24.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: 66982515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.24.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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 66982519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.24.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66982521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 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: 66982522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66982524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 66982525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66982528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 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: 66982529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '480.970.32.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: 66982530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.40.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: 66982531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66982532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66982533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 10, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.970.48.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': ['S', '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: 66982534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.48.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: 66982535
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66982536
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66982537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.970.60.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': '60.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_5', '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: 66982539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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: 66982540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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: 66982542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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: 66982544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.60.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982545
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982546
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66982547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.80.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: 66982548
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.80.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: 66982550
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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: 66982551
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 5, 'counter': 71, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '480.970.96.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: 66982552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 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: 66982553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.120.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: 66982554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.120.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: 66982555
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.120.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: 66982556
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.120.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66982557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66982558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.970.120.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.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: 66982559
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '480.970.160.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: 66982561
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 2, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.970.240.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': '240.194', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 194, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5\\times S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', '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: 66982562
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.240.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: 66982563
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.240.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: 66982564
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.970.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 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: 66982565
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.970', 'ambient_counter': 970, 'ambient_order': 480, 'ambient_tex': '\\GL(2,3):D_5', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '480.970.480.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': '480.970', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 970, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):D_5', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', '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: 66982491
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 8, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '24.d1.a1', '40.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8925, -1, 2778, -1, 2192, -1, 147, -1], 'generators': [243, 244, 96, 240], 'label': '480.970.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '240.194', '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': '60.8'}
  • id: 66982483
    {'ambient': '480.970', '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': '240.a1.a1', 'complements': ['480.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '4.b1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5592, 5440, 6495, 5440, 2796, 5832, 2924, 5832], 'generators': [1, 360, 244, 96, 6, 240, 132], 'label': '480.970.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '240.194', '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': '240.194'}
  • id: 66982484
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 6, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.g1.a1', '30.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4147, -1, 4653, -1, 4355, -1, 4836, -1], 'generators': [1, 360, 240, 6, 96], 'label': '480.970.6.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': '240.194', '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': '80.39'}
  • id: 66982485
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 6, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.i1.a1', '30.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1236, -1, 6215, -1, 7080, -1, 7194, -1], 'generators': [1, 360, 240, 18, 96], 'label': '480.970.6.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': '240.194', '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': '80.39'}
  • id: 66982486
    {'ambient': '480.970', 'aut_centralizer_order': 10, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 30, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.h1.a1', '30.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1838, -1, 8471, -1, 5095, -1, 6545, -1], 'generators': [1, 96, 120, 12, 240], 'label': '480.970.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '240.194', '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: 66982487
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 12, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.h1.a1', '12.i1.a1', '30.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [193, -1, 7859, -1, 7519, -1, 8473, -1], 'generators': [13, 120, 240, 6, 96], 'label': '480.970.6.e1.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.e1.a1', 'projective_image': '240.194', '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': '40.13'}
  • id: 66982488
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 6, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.f1.a1', '12.g1.a1', '12.h1.a1', '30.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [887, -1, 6542, -1, 6704, -1, 7571, -1], 'generators': [13, 120, 240, 18, 96], 'label': '480.970.6.f1.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.f1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 66982489
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 6, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.i1.a1', '30.g1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2982, -1, 9313, -1, 6328, -1, 5311, -1], 'generators': [243, 252, 240, 360, 96], 'label': '480.970.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 66982490
    {'ambient': '480.970', 'aut_centralizer_order': 10, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '24.b1.a1', '40.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8342, -1, 2051, -1, 298, -1, 668, -1], 'generators': [1, 96, 244, 240], 'label': '480.970.8.a1.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.a1.a1', 'projective_image': '240.194', '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: 66982492
    {'ambient': '480.970', 'aut_centralizer_order': 6, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 24, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7322, -1, 3512, -1, 1505, -1, 1504, -1], 'generators': [6, 240, 96, 244], 'label': '480.970.8.c1.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.c1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 66982493
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': ['48.c1.a1', '48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.c1.a1', '40.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4695, 2720, 8082, 2720, 1700, 2033, 3358, 2033], 'generators': [1, 240, 244, 132, 360], 'label': '480.970.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '240.194', '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': '48.48'}
  • id: 66982494
    {'ambient': '480.970', 'aut_centralizer_order': 10, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 10, 'centralizer': '48.a1.a1', 'complements': ['240.c1.a1', '240.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.d1.a1', '8.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5279, 1839, 8471, 1839, 1782, 1971, 2584, 1971], 'generators': [1, 240, 244, 132, 96, 360], 'label': '480.970.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '240.194', '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': '48.48'}
  • id: 66982495
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.f1.a1', '40.c1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5090, -1, 6618, -1, 3830, -1, 3784, -1], 'generators': [6, 240, 244, 132, 360], 'label': '480.970.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66982496
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.g1.a1', '40.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5485, -1, 9777, -1, 3404, -1, 2837, -1], 'generators': [243, 240, 244, 252, 360], 'label': '480.970.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66982497
    {'ambient': '480.970', 'aut_centralizer_order': 20, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.e1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2625, 6130, 9258, 6130, 5868, 6386, 4368, 6386], 'generators': [12, 96, 240, 360], 'label': '480.970.12.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': '240.194', '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': '48.48'}
  • id: 66982498
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.d1.a1', '24.f1.a1', '24.f1.a2', '60.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5949, -1, 2277, -1, 3375, -1, 3375, -1], 'generators': [1, 240, 96, 366], 'label': '480.970.12.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': '240.194', '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': '20.4'}
  • id: 66982499
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 24, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '60.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6517, -1, 3757, -1, 3892, -1, 3892, -1], 'generators': [1, 240, 96, 6], 'label': '480.970.12.c1.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.c1.a1', 'projective_image': '240.194', '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': '40.13'}
  • id: 66982500
    {'ambient': '480.970', 'aut_centralizer_order': 20, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '60.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4116, -1, 5012, -1, 4367, -1, 5303, -1], 'generators': [1, 96, 240, 360], 'label': '480.970.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '240.194', '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': '16.11'}
  • id: 66982501
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 24, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.e1.a1', '60.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3591, -1, 5646, -1, 5302, -1, 5870, -1], 'generators': [6, 240, 96, 12], 'label': '480.970.12.e1.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.e1.a1', 'projective_image': '240.194', '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': '40.13'}
  • id: 66982502
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 12, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '60.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1896, -1, 6052, -1, 6336, -1, 6338, -1], 'generators': [366, 240, 96, 12], 'label': '480.970.12.f1.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.f1.a1', 'projective_image': '240.194', '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': '80.39'}
  • id: 66982503
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 12, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '60.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4700, -1, 6513, -1, 4835, -1, 4836, -1], 'generators': [243, 240, 96, 12], 'label': '480.970.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '240.194', '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': '80.39'}
  • id: 66982504
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 120, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.e1.a1', '60.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [340, -1, 7809, -1, 6704, -1, 8846, -1], 'generators': [13, 120, 240, 96], 'label': '480.970.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66982505
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 2, 'centralizer': '240.a1.a1', 'complements': ['240.b1.a1', '240.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '8.c1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5907, 8161, 5797, 8161, 3073, 8747, 3263, 8747], 'generators': [6, 240, 252, 360, 244, 96], 'label': '480.970.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '240.194', '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': '240.194'}
  • id: 66982506
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 24, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.e1.a1', '60.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1026, -1, 8571, -1, 7076, -1, 8473, -1], 'generators': [123, 240, 96, 252], 'label': '480.970.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 66982507
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 60, 'centralizer': '240.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.e1.a1', '30.f1.a1', '30.g1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1213, -1, 7984, -1, 8445, -1, 7989, -1], 'generators': [1, 6, 12], 'label': '480.970.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '240.194', '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: 66982508
    {'ambient': '480.970', 'aut_centralizer_order': 60, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 240, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '80.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8641, -1, 2699, -1, 1766, -1, 1492, -1], 'generators': [240, 96, 244], 'label': '480.970.16.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': '240.194', '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': '4.2'}
  • id: 66982509
    {'ambient': '480.970', 'aut_centralizer_order': 10, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.5', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '80.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9377, -1, 676, -1, 1005, -1, 1028, -1], 'generators': [1, 244, 96], 'label': '480.970.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '480.970', '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: 66982510
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '120.36', 'aut_weyl_index': 16, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.a1.a1', '48.d1.a1', '80.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9807, -1, 1379, -1, 2134, -1, 565, -1], 'generators': [243, 96, 244], 'label': '480.970.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.c1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 66982511
    {'ambient': '480.970', 'aut_centralizer_order': 80, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '24.a1.a1', 'complements': ['24.f1.a1', '24.f1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['60.a1.a1', '80.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5121, 4444, 9418, 4444, 2713, 4086, 2713, 4086], 'generators': [244, 132, 360, 240], 'label': '480.970.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '240.194', '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: 66982512
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 80, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '5.a1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '60.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7958, -1, 4840, -1, 976, -1, 2191, -1], 'generators': [1, 6, 240, 244], 'label': '480.970.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '240.194', '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: 66982513
    {'ambient': '480.970', 'aut_centralizer_order': 48, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '120.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5477, 7778, 3785, 7778, 4744, 8747, 4765, 8747], 'generators': [6, 96, 240], 'label': '480.970.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 66982514
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 240, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '120.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6115, -1, 2130, -1, 3846, -1, 4235, -1], 'generators': [1, 96, 240], 'label': '480.970.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '240.194', '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': '4.2'}
  • id: 66982515
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 48, 'centralizer': '60.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '120.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4661, -1, 2998, -1, 5120, -1, 5142, -1], 'generators': [18, 96, 240], 'label': '480.970.24.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': '24.c1.a1', 'projective_image': '240.194', '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': '20.4'}
  • id: 66982516
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 2, 'centralizer': '240.a1.a1', 'complements': ['240.c1.a1', '240.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.g1.a1', '8.b1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6628, 5440, 9500, 5440, 3660, 5832, 1806, 5832], 'generators': [243, 240, 96, 252, 244, 360], 'label': '480.970.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '240.194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '240.194'}
  • id: 66982517
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 48, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '120.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6597, -1, 3458, -1, 4367, -1, 3714, -1], 'generators': [243, 96, 240], 'label': '480.970.24.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '240.194', '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': '20.4'}
  • id: 66982518
    {'ambient': '480.970', 'aut_centralizer_order': 80, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 240, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '120.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3706, -1, 6052, -1, 5488, -1, 6445, -1], 'generators': [12, 240, 96], 'label': '480.970.24.e1.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.e1.a1', 'projective_image': '240.194', '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': '4.2'}
  • id: 66982519
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.d1.a1', '120.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7234, -1, 579, -1, 3325, -1, 2978, -1], 'generators': [1, 96, 126], 'label': '480.970.24.f1.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.f1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66982520
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.d1.a1', '120.f1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7234, -1, 259, -1, 3325, -1, 3346, -1], 'generators': [1, 96, 366], 'label': '480.970.24.f1.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.f1.a2', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66982521
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1', '60.g1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3878, -1, 4459, -1, 7552, -1, 6805, -1], 'generators': [1, 6, 360], 'label': '480.970.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66982522
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.a1.a1'], 'contains': ['60.d1.a1', '60.f1.a1', '60.i1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1095, -1, 7438, -1, 9475, -1, 9177, -1], 'generators': [1, 18], 'label': '480.970.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '240.194', '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': '16.11'}
  • id: 66982523
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '60.h1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2031, -1, 8957, -1, 8040, -1, 7699, -1], 'generators': [1, 12], 'label': '480.970.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '240.194', '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': '16.11'}
  • id: 66982524
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 240, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '60.h1.a1', '60.i1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [765, -1, 8284, -1, 9831, -1, 9830, -1], 'generators': [13, 6], 'label': '480.970.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '240.194', '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': '8.5'}
  • id: 66982525
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.a1.a1'], 'contains': ['60.f1.a1', '60.g1.a1', '60.h1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [289, -1, 7849, -1, 9177, -1, 9475, -1], 'generators': [13, 18], 'label': '480.970.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '240.194', '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: 66982526
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.e1.a1', '60.f1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1548, -1, 6923, -1, 8838, -1, 8092, -1], 'generators': [6, 12, 360], 'label': '480.970.30.f1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66982527
    {'ambient': '480.970', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 3, 'centralizer': '240.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.e1.a1', '6.f1.a1', '6.g1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1838, -1, 6768, -1, 6328, -1, 6545, -1], 'generators': [1, 96, 12, 120, 6, 240], 'label': '480.970.3.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': '240.194', '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': '80.39'}
  • id: 66982528
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.g1.a1', '60.i1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2429, -1, 9874, -1, 8445, -1, 7294, -1], 'generators': [243, 360], 'label': '480.970.30.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.g1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66982529
    {'ambient': '480.970', 'aut_centralizer_order': 60, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 240, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'contains': ['96.a1.a1', '160.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9660, -1, 1310, -1, 2068, -1, 1492, -1], 'generators': [244, 96], 'label': '480.970.32.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': '480.970', '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': '4.2'}
  • id: 66982530
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '10.a1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '120.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7832, -1, 2390, -1, 1435, -1, 2121, -1], 'generators': [1, 240, 244], 'label': '480.970.40.a1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '40.a1.a1', 'projective_image': '240.194', '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: 66982531
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 160, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '10.c1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '120.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8714, -1, 6024, -1, 2469, -1, 1823, -1], 'generators': [243, 240, 244], 'label': '480.970.40.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.194', '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': '12.4'}
  • id: 66982532
    {'ambient': '480.970', 'aut_centralizer_order': 24, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '40.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '10.b1.a1', '20.b1.a1'], 'contains': ['80.a1.a1', '120.e1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7234, -1, 5232, -1, 2957, -1, 2452, -1], 'generators': [6, 244, 240], 'label': '480.970.40.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.c1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66982533
    {'ambient': '480.970', 'aut_centralizer_order': 480, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5857, 7069, 3545, 7107, 4227, 7207, 3971, 7207], 'generators': [240, 96], 'label': '480.970.48.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': '240.194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66982534
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.b1.a1', '24.f1.a1', '24.f1.a2'], 'contains': ['96.a1.a1', '240.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8012, -1, 126, -1, 3267, -1, 3309, -1], 'generators': [1, 96], 'label': '480.970.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '480.970', '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': '2.1'}
  • id: 66982535
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '60.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.a1', '24.f1.a2'], 'contains': ['96.a1.a1', '240.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5520, -1, 550, -1, 3896, -1, 3640, -1], 'generators': [18, 96], 'label': '480.970.48.c1.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.c1.a1', 'projective_image': '480.970', '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': '10.1'}
  • id: 66982536
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.d1.a1', '24.f1.a1', '24.f1.a2'], 'contains': ['96.a1.a1', '240.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8530, -1, 1450, -1, 3598, -1, 2978, -1], 'generators': [243, 96], 'label': '480.970.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66982537
    {'ambient': '480.970', 'aut_centralizer_order': 80, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.c1.a1', '30.f1.a1', '30.g1.a1'], 'contains': ['120.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2724, 5307, 9129, 5229, 7039, 5565, 6114, 5565], 'generators': [12, 360], 'label': '480.970.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 30, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '240.194', '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: 66982538
    {'ambient': '480.970', 'aut_centralizer_order': 20, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': ['120.f1.a1', '120.f1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['12.a1.a1', '16.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5773, 5440, 9500, 5440, 2630, 5154, 2063, 5154], 'generators': [244, 252, 360, 96, 240], 'label': '480.970.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '240.194', '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': '48.48'}
  • id: 66982539
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.c1.a1', '120.f1.a1', '120.f1.a2'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4185, -1, 2724, -1, 5840, -1, 5498, -1], 'generators': [1, 366, 240], 'label': '480.970.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '240.194', '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: 66982540
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.c1.a1', '120.e1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5397, -1, 4016, -1, 6158, -1, 5816, -1], 'generators': [1, 6], 'label': '480.970.60.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '240.194', '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: 66982541
    {'ambient': '480.970', 'aut_centralizer_order': 80, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3188, -1, 4577, -1, 6741, -1, 7074, -1], 'generators': [1, 360], 'label': '480.970.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '240.194', '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: 66982542
    {'ambient': '480.970', 'aut_centralizer_order': 32, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.a1.a1', '30.d1.a1', '30.f1.a1'], 'contains': ['120.b1.a1', '120.d1.a1', '120.e1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2233, -1, 5699, -1, 7767, -1, 7505, -1], 'generators': [6, 12], 'label': '480.970.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '240.194', '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: 66982543
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.b1.a1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.b1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [232, -1, 6754, -1, 8197, -1, 8014, -1], 'generators': [366, 12], 'label': '480.970.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '240.194', '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: 66982544
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '30.a1.a1', '30.e1.a1', '30.g1.a1'], 'contains': ['120.c1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3859, -1, 7431, -1, 7337, -1, 6776, -1], 'generators': [243, 12], 'label': '480.970.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '240.194', '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': '8.3'}
  • id: 66982545
    {'ambient': '480.970', 'aut_centralizer_order': 160, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '30.c1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [627, -1, 8395, -1, 8495, -1, 8846, -1], 'generators': [13], 'label': '480.970.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.h1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66982546
    {'ambient': '480.970', 'aut_centralizer_order': 32, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '60.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '30.b1.a1', '30.d1.a1', '30.g1.a1'], 'contains': ['120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1355, -1, 9471, -1, 8793, -1, 8473, -1], 'generators': [123], 'label': '480.970.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.i1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66982547
    {'ambient': '480.970', 'aut_centralizer_order': 240, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '20.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'contains': ['160.a1.a1', '240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7333, -1, 5189, -1, 2696, -1, 2419, -1], 'generators': [240, 244], 'label': '480.970.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.194', '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: 66982548
    {'ambient': '480.970', 'aut_centralizer_order': 40, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 320, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '40.a1.a1'], 'contains': ['160.a1.a1', '240.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9127, -1, 1350, -1, 1588, -1, 2121, -1], 'generators': [1, 244], 'label': '480.970.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '480.970', '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: 66982549
    {'ambient': '480.970', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 4, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.c1.a1', '20.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7556, -1, 3728, -1, 1270, -1, 1384, -1], 'generators': [1, 240, 244, 6, 96], 'label': '480.970.4.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': '240.194', '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': '60.8'}
  • id: 66982550
    {'ambient': '480.970', 'aut_centralizer_order': 8, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 320, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '40.b1.a1'], 'contains': ['160.a1.a1', '240.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9403, -1, 2987, -1, 2399, -1, 1823, -1], 'generators': [243, 244], 'label': '480.970.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.c1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66982551
    {'ambient': '480.970', 'aut_centralizer_order': 480, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '2.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.d1.a1'], 'contains': ['480.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8127, 7414, 1008, 6283, 3610, 7207, 3474, 7207], 'generators': [96], 'label': '480.970.96.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': '480.970', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.29', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66982552
    {'ambient': '480.970', 'aut_centralizer_order': 160, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.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': 6, 'diagramx': [4562, -1, 2332, -1, 4917, -1, 5341, -1], 'generators': [1, 240], 'label': '480.970.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.a1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66982553
    {'ambient': '480.970', 'aut_centralizer_order': 64, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.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': 15, 'diagramx': [2375, -1, 3328, -1, 5893, -1, 5978, -1], 'generators': [18, 240], 'label': '480.970.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '240.194', '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: 66982554
    {'ambient': '480.970', 'aut_centralizer_order': 32, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.b1.a1', '60.b1.a1', '60.c1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6413, -1, 5344, -1, 5257, -1, 5001, -1], 'generators': [243, 240], 'label': '480.970.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.194', '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: 66982555
    {'ambient': '480.970', 'aut_centralizer_order': 320, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.a1.a1', '60.d1.a1', '60.e1.a1', '60.f1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2816, -1, 7233, -1, 7337, -1, 7074, -1], 'generators': [12], 'label': '480.970.120.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': '240.194', '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: 66982556
    {'ambient': '480.970', 'aut_centralizer_order': 192, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '10.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.c1.a1', '60.c1.a1', '60.e1.a1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5435, -1, 3954, -1, 5575, -1, 5659, -1], 'generators': [6], 'label': '480.970.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '240.194', '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': '2.1'}
  • id: 66982557
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '60.b1.a1'], 'contains': ['240.b1.a1', '240.c1.a1', '240.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6099, -1, 1335, -1, 4578, -1, 4322, -1], 'generators': [1, 126], 'label': '480.970.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.f1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66982558
    {'ambient': '480.970', 'aut_centralizer_order': 16, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a2', '60.b1.a1'], 'contains': ['240.b1.a1', '240.c1.a1', '240.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6099, -1, 1040, -1, 4578, -1, 4662, -1], 'generators': [1, 366], 'label': '480.970.120.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.f1.a2', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66982559
    {'ambient': '480.970', 'aut_centralizer_order': 240, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9178, -1, 2746, -1, 2399, -1, 2121, -1], 'generators': [244], 'label': '480.970.160.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': '480.970', '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: 66982560
    {'ambient': '480.970', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 20, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.a1.a1', '20.b1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4941, -1, 7104, -1, 2523, -1, 3814, -1], 'generators': [1, 240, 360, 6, 244, 132], 'label': '480.970.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '240.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66982561
    {'ambient': '480.970', 'aut_centralizer_order': 1920, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, '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.d1.a1', '120.e1.a1'], 'contains': ['480.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5098, 6360, 3681, 5229, 5087, 5729, 5171, 5729], 'generators': [240], 'label': '480.970.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': -120, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '60.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.194', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.194', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66982562
    {'ambient': '480.970', 'aut_centralizer_order': 160, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.b1.a1', '120.a1.a1', '120.f1.a1', '120.f1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7836, -1, 918, -1, 3950, -1, 4322, -1], 'generators': [1], 'label': '480.970.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '240.b1.a1', 'projective_image': '480.970', '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: 66982563
    {'ambient': '480.970', 'aut_centralizer_order': 64, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '120.b1.a1', '120.f1.a1', '120.f1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4415, -1, 1464, -1, 4566, -1, 4620, -1], 'generators': [18], 'label': '480.970.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '480.970', '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: 66982564
    {'ambient': '480.970', 'aut_centralizer_order': 32, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '80.c1.a1', '120.c1.a1', '120.f1.a1', '120.f1.a2'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8337, -1, 1806, -1, 4247, -1, 4024, -1], 'generators': [243], 'label': '480.970.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '480.970', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66982565
    {'ambient': '480.970', '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.d1.a1'], 'contains': [], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7981, 6897, 1669, 5766, 4099, 6468, 4173, 6468], 'generators': [], 'label': '480.970.480.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': '480.970', '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: 66982566
    {'ambient': '480.970', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 2, 'centralizer': '240.a1.a1', 'complements': ['80.b1.a1', '80.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '30.f1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2532, 7816, 5797, 7816, 5844, 8747, 5796, 8747], 'generators': [6, 360, 240, 12, 96], 'label': '480.970.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '240.194', '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': '240.194'}