Abstract group data - 960.10966

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [12, 2, 2, 4, 2, 2, 2, 4, 10, 10], 'aut_gens': [[1, 2, 4, 24, 48], [9, 2, 4, 720, 168], [745, 2, 748, 24, 528], [481, 482, 244, 504, 528], [745, 2, 28, 504, 816], [481, 2, 436, 504, 912], [1, 482, 244, 504, 528], [265, 482, 748, 24, 528], [265, 2, 556, 24, 144], [17, 2, 788, 504, 72], [481, 2, 52, 504, 528]], 'aut_group': '3840.ho', 'aut_hash': 4584141657853489991, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3840, 'aut_permdeg': 24, 'aut_perms': [2253843814588285215111, 859805579988956793, 738228385321419513, 541662136986560154149328, 26007844155662101356959, 49698488061513, 859809503011335033, 131510761342195356592763, 129261184634863016844633, 129260205382678702959753], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 10, 1, 1], [2, 12, 1, 2], [2, 30, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 6, 1, 2], [4, 10, 1, 1], [4, 30, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [6, 16, 1, 1], [6, 80, 1, 1], [8, 6, 2, 1], [8, 12, 1, 1], [8, 60, 1, 2], [10, 2, 2, 1], [10, 2, 4, 1], [10, 24, 2, 2], [12, 80, 1, 1], [15, 16, 2, 1], [20, 12, 2, 2], [30, 16, 2, 1], [30, 16, 4, 1], [40, 12, 4, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3\\times F_5\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', '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, 2, 1], [2, 10, 1], [2, 12, 2], [2, 30, 1], [2, 60, 1], [3, 8, 1], [4, 6, 2], [4, 10, 1], [4, 30, 1], [4, 60, 1], [5, 2, 2], [6, 8, 1], [6, 16, 1], [6, 80, 1], [8, 6, 2], [8, 12, 1], [8, 60, 2], [10, 2, 6], [10, 24, 4], [12, 80, 1], [15, 16, 2], [20, 12, 4], [30, 16, 6], [40, 12, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '480.1193', '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', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10966, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 10, 1, 1], [2, 12, 1, 2], [2, 30, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 6, 1, 2], [4, 10, 1, 1], [4, 30, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [6, 16, 1, 1], [6, 80, 1, 1], [8, 6, 2, 1], [8, 12, 1, 1], [8, 60, 1, 2], [10, 2, 2, 1], [10, 2, 4, 1], [10, 24, 2, 2], [12, 80, 1, 1], [15, 16, 2, 1], [20, 12, 2, 2], [30, 16, 2, 1], [30, 16, 4, 1], [40, 12, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 60480, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 8], [8, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '480.1193', 'hash': 10966, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 6, 2, 10], 'inner_gens': [[1, 2, 20, 240, 792], [1, 2, 484, 24, 48], [9, 482, 4, 720, 936], [265, 2, 748, 24, 528], [745, 2, 124, 504, 48]], 'inner_hash': 1193, 'inner_nilpotent': False, 'inner_order': 480, 'inner_split': True, 'inner_tex': 'D_{10}\\times S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 4, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 12], [3, 8], [4, 14], [6, 8], [8, 5]], 'label': '960.10966', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 8, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'GL(2,3):D10', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 37, 'number_conjugacy_classes': 55, 'number_divisions': 34, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 298, 'number_subgroup_classes': 304, 'number_subgroups': 2918, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 127], [3, 8], [4, 112], [5, 4], [6, 104], [8, 144], [10, 108], [12, 80], [15, 32], [20, 48], [30, 96], [40, 96]], '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, 2, 244, 504, 528], [1, 2, 4, 24, 816]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [3, 8], [4, 4], [8, 4], [12, 4], [32, 2]], 'representations': {'PC': {'code': 8593022825841698262663120202750109516673799501984128795148547, 'gens': [1, 2, 3, 5, 6], 'pres': [8, -2, -2, -2, -3, -2, 2, -2, -5, 482, 5818, 66, 515, 9604, 7220, 1348, 836, 38021, 11253, 1901, 1093, 141, 12118, 166, 12311]}, 'Perm': {'d': 21, 'gens': [2459999639040975367, 40949162930149200, 493359947036732880, 9270329331605040, 37, 5496238066015801440, 8074576096790193360, 10271542109627555280]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_{10}', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 142600342
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10966, 'group_order': 960, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 142600353
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 10966, 'group_order': 960, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 480, 'size': 1}
  • id: 142600364
    {'aut_label': '2B', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 10966, 'group_order': 960, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2, 'size': 2}
  • id: 142600375
    {'aut_label': '2C', 'centralizer': '10.d1.a1', 'counter': 4, 'group_counter': 10966, 'group_order': 960, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 108, 'size': 10}
  • id: 142600386
    {'aut_label': '2D', 'centralizer': '12.d1.a1', 'counter': 5, 'group_counter': 10966, 'group_order': 960, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 1, 'size': 12}
  • id: 142600393
    {'aut_label': '2E', 'centralizer': '12.f1.a1', 'counter': 6, 'group_counter': 10966, 'group_order': 960, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 3, 'size': 12}
  • id: 142600394
    {'aut_label': '2F', 'centralizer': '30.n1.a1', 'counter': 7, 'group_counter': 10966, 'group_order': 960, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 62, 'size': 30}
  • id: 142600395
    {'aut_label': '2G', 'centralizer': '60.j1.a1', 'counter': 8, 'group_counter': 10966, 'group_order': 960, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 821, 'size': 60}
  • id: 142600396
    {'aut_label': '3A', 'centralizer': '8.b1.a1', 'counter': 9, 'group_counter': 10966, 'group_order': 960, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 8, 'size': 8}
  • id: 142600343
    {'aut_label': '4A', 'centralizer': '6.f1.a1', 'counter': 10, 'group_counter': 10966, 'group_order': 960, 'label': '4A', 'order': 4, 'powers': [2, 10, 10], 'representative': 242, 'size': 6}
  • id: 142600344
    {'aut_label': '4B', 'centralizer': '6.c1.a1', 'counter': 11, 'group_counter': 10966, 'group_order': 960, 'label': '4B', 'order': 4, 'powers': [2, 11, 11], 'representative': 264, 'size': 6}
  • id: 142600345
    {'aut_label': '4C', 'centralizer': '10.f1.a1', 'counter': 12, 'group_counter': 10966, 'group_order': 960, 'label': '4C', 'order': 4, 'powers': [2, 12, 12], 'representative': 494, 'size': 10}
  • id: 142600346
    {'aut_label': '4D', 'centralizer': '30.j1.a1', 'counter': 13, 'group_counter': 10966, 'group_order': 960, 'label': '4D', 'order': 4, 'powers': [2, 13, 13], 'representative': 60, 'size': 30}
  • id: 142600347
    {'aut_label': '4E', 'centralizer': '60.q1.a1', 'counter': 14, 'group_counter': 10966, 'group_order': 960, 'label': '4E', 'order': 4, 'powers': [2, 14, 14], 'representative': 375, 'size': 60}
  • id: 142600348
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 10966, 'group_order': 960, 'label': '5A1', 'order': 5, 'powers': [16, 16, 1], 'representative': 384, 'size': 2}
  • id: 142600349
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 10966, 'group_order': 960, 'label': '5A2', 'order': 5, 'powers': [15, 15, 1], 'representative': 768, 'size': 2}
  • id: 142600350
    {'aut_label': '6A', 'centralizer': '8.b1.a1', 'counter': 17, 'group_counter': 10966, 'group_order': 960, 'label': '6A', 'order': 6, 'powers': [9, 2, 17], 'representative': 496, 'size': 8}
  • id: 142600351
    {'aut_label': '6B', 'centralizer': '16.a1.a1', 'counter': 18, 'group_counter': 10966, 'group_order': 960, 'label': '6B', 'order': 6, 'powers': [9, 3, 18], 'representative': 18, 'size': 16}
  • id: 142600352
    {'aut_label': '6C', 'centralizer': '80.b1.a1', 'counter': 19, 'group_counter': 10966, 'group_order': 960, 'label': '6C', 'order': 6, 'powers': [9, 4, 19], 'representative': 604, 'size': 80}
  • id: 142600354
    {'aut_label': '8A1', 'centralizer': '6.c1.a1', 'counter': 20, 'group_counter': 10966, 'group_order': 960, 'label': '8A1', 'order': 8, 'powers': [11, 20, 21], 'representative': 721, 'size': 6}
  • id: 142600355
    {'aut_label': '8A1', 'centralizer': '6.c1.a1', 'counter': 21, 'group_counter': 10966, 'group_order': 960, 'label': '8A-1', 'order': 8, 'powers': [11, 21, 20], 'representative': 25, 'size': 6}
  • id: 142600356
    {'aut_label': '8B', 'centralizer': '12.j1.a1', 'counter': 22, 'group_counter': 10966, 'group_order': 960, 'label': '8B', 'order': 8, 'powers': [11, 22, 22], 'representative': 723, 'size': 12}
  • id: 142600357
    {'aut_label': '8C', 'centralizer': '60.bc1.a1', 'counter': 23, 'group_counter': 10966, 'group_order': 960, 'label': '8C', 'order': 8, 'powers': [11, 23, 23], 'representative': 159, 'size': 60}
  • id: 142600358
    {'aut_label': '8D', 'centralizer': '60.n1.a1', 'counter': 24, 'group_counter': 10966, 'group_order': 960, 'label': '8D', 'order': 8, 'powers': [11, 24, 24], 'representative': 805, 'size': 60}
  • id: 142600359
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 25, 'group_counter': 10966, 'group_order': 960, 'label': '10A1', 'order': 10, 'powers': [16, 26, 2], 'representative': 96, 'size': 2}
  • id: 142600360
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 26, 'group_counter': 10966, 'group_order': 960, 'label': '10A3', 'order': 10, 'powers': [15, 25, 2], 'representative': 288, 'size': 2}
  • id: 142600361
    {'aut_label': '10B1', 'centralizer': '2.b1.a1', 'counter': 27, 'group_counter': 10966, 'group_order': 960, 'label': '10B1', 'order': 10, 'powers': [16, 29, 3], 'representative': 578, 'size': 2}
  • id: 142600362
    {'aut_label': '10B1', 'centralizer': '2.b1.a1', 'counter': 28, 'group_counter': 10966, 'group_order': 960, 'label': '10B-1', 'order': 10, 'powers': [16, 30, 3], 'representative': 386, 'size': 2}
  • id: 142600363
    {'aut_label': '10B1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 10966, 'group_order': 960, 'label': '10B3', 'order': 10, 'powers': [15, 28, 3], 'representative': 770, 'size': 2}
  • id: 142600365
    {'aut_label': '10B1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 10966, 'group_order': 960, 'label': '10B-3', 'order': 10, 'powers': [15, 27, 3], 'representative': 194, 'size': 2}
  • id: 142600366
    {'aut_label': '10C1', 'centralizer': '24.c1.a1', 'counter': 31, 'group_counter': 10966, 'group_order': 960, 'label': '10C1', 'order': 10, 'powers': [15, 32, 5], 'representative': 193, 'size': 24}
  • id: 142600367
    {'aut_label': '10C1', 'centralizer': '24.c1.a1', 'counter': 32, 'group_counter': 10966, 'group_order': 960, 'label': '10C3', 'order': 10, 'powers': [16, 31, 5], 'representative': 97, 'size': 24}
  • id: 142600368
    {'aut_label': '10D1', 'centralizer': '24.c1.a1', 'counter': 33, 'group_counter': 10966, 'group_order': 960, 'label': '10D1', 'order': 10, 'powers': [15, 34, 6], 'representative': 195, 'size': 24}
  • id: 142600369
    {'aut_label': '10D1', 'centralizer': '24.c1.a1', 'counter': 34, 'group_counter': 10966, 'group_order': 960, 'label': '10D3', 'order': 10, 'powers': [16, 33, 6], 'representative': 99, 'size': 24}
  • id: 142600370
    {'aut_label': '12A', 'centralizer': '80.f1.a1', 'counter': 35, 'group_counter': 10966, 'group_order': 960, 'label': '12A', 'order': 12, 'powers': [17, 12, 35], 'representative': 46, 'size': 80}
  • id: 142600371
    {'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 36, 'group_counter': 10966, 'group_order': 960, 'label': '15A1', 'order': 15, 'powers': [37, 15, 9], 'representative': 208, 'size': 16}
  • id: 142600372
    {'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 37, 'group_counter': 10966, 'group_order': 960, 'label': '15A2', 'order': 15, 'powers': [36, 16, 9], 'representative': 392, 'size': 16}
  • id: 142600373
    {'aut_label': '20A1', 'centralizer': '12.j1.a1', 'counter': 38, 'group_counter': 10966, 'group_order': 960, 'label': '20A1', 'order': 20, 'powers': [25, 39, 10], 'representative': 50, 'size': 12}
  • id: 142600374
    {'aut_label': '20A1', 'centralizer': '12.j1.a1', 'counter': 39, 'group_counter': 10966, 'group_order': 960, 'label': '20A3', 'order': 20, 'powers': [26, 38, 10], 'representative': 146, 'size': 12}
  • id: 142600376
    {'aut_label': '20B1', 'centralizer': '12.j1.a1', 'counter': 40, 'group_counter': 10966, 'group_order': 960, 'label': '20B1', 'order': 20, 'powers': [26, 41, 11], 'representative': 840, 'size': 12}
  • id: 142600377
    {'aut_label': '20B1', 'centralizer': '12.j1.a1', 'counter': 41, 'group_counter': 10966, 'group_order': 960, 'label': '20B3', 'order': 20, 'powers': [25, 40, 11], 'representative': 552, 'size': 12}
  • id: 142600378
    {'aut_label': '30A1', 'centralizer': '16.a1.a1', 'counter': 42, 'group_counter': 10966, 'group_order': 960, 'label': '30A1', 'order': 30, 'powers': [36, 26, 17], 'representative': 104, 'size': 16}
  • id: 142600379
    {'aut_label': '30A1', 'centralizer': '16.a1.a1', 'counter': 43, 'group_counter': 10966, 'group_order': 960, 'label': '30A7', 'order': 30, 'powers': [37, 25, 17], 'representative': 56, 'size': 16}
  • id: 142600380
    {'aut_label': '30B1', 'centralizer': '16.a1.a1', 'counter': 44, 'group_counter': 10966, 'group_order': 960, 'label': '30B1', 'order': 30, 'powers': [37, 27, 18], 'representative': 202, 'size': 16}
  • id: 142600381
    {'aut_label': '30B1', 'centralizer': '16.a1.a1', 'counter': 45, 'group_counter': 10966, 'group_order': 960, 'label': '30B-1', 'order': 30, 'powers': [37, 28, 18], 'representative': 66, 'size': 16}
  • id: 142600382
    {'aut_label': '30B1', 'centralizer': '16.a1.a1', 'counter': 46, 'group_counter': 10966, 'group_order': 960, 'label': '30B7', 'order': 30, 'powers': [36, 30, 18], 'representative': 106, 'size': 16}
  • id: 142600383
    {'aut_label': '30B1', 'centralizer': '16.a1.a1', 'counter': 47, 'group_counter': 10966, 'group_order': 960, 'label': '30B-7', 'order': 30, 'powers': [36, 29, 18], 'representative': 586, 'size': 16}
  • id: 142600384
    {'aut_label': '40A1', 'centralizer': '12.j1.a1', 'counter': 48, 'group_counter': 10966, 'group_order': 960, 'label': '40A1', 'order': 40, 'powers': [40, 50, 20], 'representative': 49, 'size': 12}
  • id: 142600385
    {'aut_label': '40A1', 'centralizer': '12.j1.a1', 'counter': 49, 'group_counter': 10966, 'group_order': 960, 'label': '40A-1', 'order': 40, 'powers': [40, 51, 21], 'representative': 57, 'size': 12}
  • id: 142600387
    {'aut_label': '40A1', 'centralizer': '12.j1.a1', 'counter': 50, 'group_counter': 10966, 'group_order': 960, 'label': '40A3', 'order': 40, 'powers': [41, 48, 20], 'representative': 409, 'size': 12}
  • id: 142600388
    {'aut_label': '40A1', 'centralizer': '12.j1.a1', 'counter': 51, 'group_counter': 10966, 'group_order': 960, 'label': '40A-3', 'order': 40, 'powers': [41, 49, 21], 'representative': 145, 'size': 12}
  • id: 142600389
    {'aut_label': '40B1', 'centralizer': '12.j1.a1', 'counter': 52, 'group_counter': 10966, 'group_order': 960, 'label': '40B1', 'order': 40, 'powers': [40, 53, 22], 'representative': 51, 'size': 12}
  • id: 142600390
    {'aut_label': '40B1', 'centralizer': '12.j1.a1', 'counter': 53, 'group_counter': 10966, 'group_order': 960, 'label': '40B3', 'order': 40, 'powers': [41, 54, 22], 'representative': 123, 'size': 12}
  • id: 142600391
    {'aut_label': '40B1', 'centralizer': '12.j1.a1', 'counter': 54, 'group_counter': 10966, 'group_order': 960, 'label': '40B9', 'order': 40, 'powers': [40, 55, 22], 'representative': 219, 'size': 12}
  • id: 142600392
    {'aut_label': '40B1', 'centralizer': '12.j1.a1', 'counter': 55, 'group_counter': 10966, 'group_order': 960, 'label': '40B13', 'order': 40, 'powers': [41, 52, 22], 'representative': 147, '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: 13445955
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445966
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445977
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445983
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445984
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445985
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445986
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445987
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445988
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 0, -1, 2, 2, 2, 2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445956
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 2, 0, -1, -2, 2, 2, -2, 0, 2, 2, -1, 1, 1, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, -1, -1, -1, -2, -2, 2, 2, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445957
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, 0, -2, 0, -1, -2, 2, -2, 2, 0, 2, 2, -1, 1, -1, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 1, -1, -1, -2, -2, 2, 2, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445958
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 0, -2, 0, -1, 2, 2, -2, -2, 0, 2, 2, -1, -1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445963
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 1, 1, -1, 1, 0, -1, -1, 3, -1, 1, 3, 3, 0, 0, 0, -1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445964
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 0, -1, -1, 3, -1, -1, 3, 3, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445965
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, 1, -1, 1, 0, 1, -1, 3, 1, -1, 3, 3, 0, 0, 0, 1, 1, -1, 1, -1, -3, 3, -3, -3, -3, 3, -1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445967
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 1, -1, -1, -1, 0, 1, -1, 3, 1, 1, 3, 3, 0, 0, 0, -1, -1, 1, -1, 1, -3, 3, -3, -3, -3, 3, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445968
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, 3, -1, 1, 1, -1, 0, 1, -1, -3, -1, 1, 3, 3, 0, 0, 0, 1, 1, -1, -1, 1, -3, 3, -3, -3, -3, 3, -1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445969
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, 3, 1, -1, 1, 1, 0, 1, -1, -3, -1, -1, 3, 3, 0, 0, 0, -1, -1, 1, 1, -1, -3, 3, -3, -3, -3, 3, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445970
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, -1, -1, 1, 1, 0, -1, -1, -3, 1, 1, 3, 3, 0, 0, 0, 1, 1, 1, -1, -1, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445971
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, 1, 1, 1, -1, 0, -1, -1, -3, 1, -1, 3, 3, 0, 0, 0, -1, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445959
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2e', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 0, 0, 0, -1, -1, 4, 4, 0, 4, 4, 4, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445960
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2f', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -4, 4, 0, 0, 4, -4, 4, 0, 0, 0, -1, -1, 4, -4, 0, -4, -4, 4, 0, 0, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445961
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2g', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, -4, 0, 0, 4, -4, 4, 0, 0, 0, -1, -1, 4, -4, 0, 4, 4, -4, 0, 0, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445962
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.2h', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -4, -4, 0, 0, 4, 4, 4, 0, 0, 0, -1, -1, 4, 4, 0, -4, -4, -4, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445972
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.4a', 'multiplicity': 2, 'nt': [15, 7], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, 0, 0, 0, -4, 8, 8, 0, 0, 0, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445973
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.4b', 'multiplicity': 2, 'nt': [30, 21], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, 0, 0, -4, -8, 8, 0, 0, 0, -2, -2, -4, 4, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 1, 1, 2, 2, -2, -2, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445974
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.4c', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445981
    {'cdim': 8, 'counter': 33, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.8a', 'multiplicity': 1, 'nt': [16, 422], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, -2, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445976
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.6a', 'multiplicity': 2, 'nt': [20, 69], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 4, 4, 0, 0, 0, -4, -4, 0, 0, 0, -3, -3, 0, 0, 0, -4, -4, -4, 0, 0, -3, -3, -3, -3, -3, -3, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13445978
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.6b', 'multiplicity': 2, 'nt': [30, 54], 'qdim': 12, 'qvalues': [12, 12, 12, 0, -4, -4, 0, 0, 0, -4, -4, 0, 0, 0, -3, -3, 0, 0, 0, 4, 4, 4, 0, 0, -3, -3, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13445979
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.6c', 'multiplicity': 2, 'nt': [30, 109], 'qdim': 12, 'qvalues': [12, 12, -12, 0, -4, 4, 0, 0, 0, 4, -4, 0, 0, 0, -3, -3, 0, 0, 0, 4, 4, -4, 0, 0, 3, -3, 3, 3, 3, -3, 1, 1, -1, -1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 13445980
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.6d', 'multiplicity': 2, 'nt': [30, 109], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 4, -4, 0, 0, 0, 4, -4, 0, 0, 0, -3, -3, 0, 0, 0, -4, -4, 4, 0, 0, 3, -3, 3, 3, 3, -3, -1, -1, 1, 1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 13445975
    {'cdim': 4, 'counter': 28, 'faithful': True, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.4d', 'multiplicity': 8, 'nt': [240, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -8, -8, 16, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13445982
    {'cdim': 8, 'counter': 34, 'faithful': True, 'group': '960.10966', 'group_order': 960, 'image': None, 'label': '960.10966.8b', 'multiplicity': 4, 'nt': [80, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 31782534
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 960, 'label': '960.10966.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 31782545
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 480, 'label': '960.10966.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 31782556
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 480, 'label': '960.10966.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 31782567
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 480, 'label': '960.10966.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 31782578
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 480, 'label': '960.10966.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 31782585
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 480, 'label': '960.10966.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 31782586
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 480, 'label': '960.10966.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 31782587
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 480, 'label': '960.10966.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 31782588
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 160, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 160, 'label': '960.10966.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782535
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 160, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 80, 'label': '960.10966.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782536
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 160, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 80, 'label': '960.10966.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782537
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 160, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 80, 'label': '960.10966.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782538
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 13, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 96, 'label': '960.10966.2e1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[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, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 31782539
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 14, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 96, 'label': '960.10966.2e2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 31782540
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 15, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.c1.a1', 'kernel_order': 48, 'label': '960.10966.2f1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[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, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 31782541
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 16, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.c1.a1', 'kernel_order': 48, 'label': '960.10966.2f2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 31782542
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 17, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.b1.a1', 'kernel_order': 48, 'label': '960.10966.2g1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[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, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 31782543
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 18, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.b1.a1', 'kernel_order': 48, 'label': '960.10966.2g2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[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, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 31782544
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 19, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 48, 'label': '960.10966.2h1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[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, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 31782546
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 96, 'counter': 20, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 48, 'label': '960.10966.2h2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 31782547
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 40, 'label': '960.10966.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 31782548
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 40, 'label': '960.10966.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 31782549
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 20, 'label': '960.10966.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 31782550
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 20, 'label': '960.10966.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 31782551
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 20, 'label': '960.10966.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 31782552
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 20, 'label': '960.10966.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 31782553
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 20, 'label': '960.10966.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 31782554
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 40, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 20, 'label': '960.10966.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 31782555
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 16, 'label': '960.10966.4a1', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782557
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 16, 'label': '960.10966.4a2', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782558
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '120.42', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 8, 'label': '960.10966.4b1', 'nt': [30, 21], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782559
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '120.42', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 8, 'label': '960.10966.4b2', 'nt': [30, 21], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782560
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 10, 'counter': 33, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 5, 'label': '960.10966.4c1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]]]}
  • id: 31782561
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 10, 'counter': 34, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 5, 'label': '960.10966.4c2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]]]}
  • id: 31782562
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d1', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[-2, 8], [-2, -8]], [[2, 8], [2, 12]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, 12]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[-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, 5], [-1, 7], [-1, 9]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]]]}
  • id: 31782563
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d2', 'nt': [240, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, -8]], [[-2, 8], [-2, 12]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[2, 8], [2, 12]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-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, 5], [1, 7], [1, 9]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]]]}
  • id: 31782564
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d3', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, -8]], [[-2, 8], [-2, 12]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[2, 8], [2, 12]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[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, 5], [-1, 7], [-1, 9]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]]]}
  • id: 31782565
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d4', 'nt': [240, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[-2, 8], [-2, -8]], [[2, 8], [2, 12]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, 12]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[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, 5], [1, 7], [1, 9]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]]]}
  • id: 31782566
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d5', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, 12]], [[2, 4], [2, -4]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[2, 8], [2, 12]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[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, 7], [1, 9], [1, 15]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]]]}
  • id: 31782568
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d6', 'nt': [240, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, 12]], [[2, 4], [2, -4]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, 12]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[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, 7], [-1, 9], [-1, 15]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [-1, 7], [-1, 9], [2, 13]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [1, 9], [-2, 11], [1, 15]]]}
  • id: 31782569
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d7', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, 12]], [[2, 4], [2, -4]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, 12]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[-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, 7], [1, 9], [1, 15]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[-1, 1], [1, 3], [-1, 7], [-1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]]]}
  • id: 31782570
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 40, 'dim': 4, 'faithful': True, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.4d8', 'nt': [240, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, 12]], [[2, 4], [2, -4]], [[2, 0], [-4, 4], [2, 8], [-2, 12]], [[2, 8], [2, 12]], [[-2, 0], [4, 4], [-2, 8], [2, 12]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 0], [-2, 4], [1, 8], [-1, 12]], [[-1, 8], [-1, 12]], [[-1, 0], [2, 4], [-1, 8], [1, 12]], [[1, 8], [1, 12]], [[-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, 7], [-1, 9], [-1, 15]], [[-1, 1], [1, 3], [1, 5], [-1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [1, 7], [1, 9], [-2, 13]], [[1, 1], [-1, 3], [-1, 5], [1, 7], [1, 9]], [[1, 1], [-1, 3], [1, 7], [1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [-1, 9], [2, 11], [-1, 15]]]}
  • id: 31782571
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 43, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 4, 'label': '960.10966.6a1', 'nt': [20, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 31782572
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 4, 'label': '960.10966.6a2', 'nt': [20, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 31782573
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 4, 'label': '960.10966.6b1', 'nt': [30, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 31782574
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '240.194', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 4, 'label': '960.10966.6b2', 'nt': [30, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 31782575
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '480.1193', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10966.6c1', 'nt': [30, 109], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 31782576
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '480.1193', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10966.6c2', 'nt': [30, 109], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 31782577
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '480.1193', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10966.6d1', 'nt': [30, 109], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 31782579
    {'center': '240.a1.a1', 'center_index': 240, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '480.1193', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10966.6d2', 'nt': [30, 109], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 31782580
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 10, 'counter': 51, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 5, 'label': '960.10966.8a', 'nt': [16, 422], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782581
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 52, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.8b1', 'nt': [80, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [4, -2]], [[-4, 1], [-4, -1]], [[4, 0], [8, 1], [4, 2], [4, -2]], [[4, 2], [-4, -2]], [[-4, 0], [-8, 1], [-4, 2], [-4, -2]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782582
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 53, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.8b2', 'nt': [80, 4], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-4, 0], [-8, 1], [-4, 2], [-4, -2]], [[-4, 2], [4, -2]], [[4, 0], [8, 1], [4, 2], [4, -2]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782583
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 54, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.8b3', 'nt': [80, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-8, 1], [-4, 2], [-4, -2]], [[-4, 2], [-4, -2]], [[-4, 2], [4, -2]], [[4, 0], [8, 1], [4, 2], [4, -2]], [[4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31782584
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 2, 'counter': 55, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '960.10966', 'group_counter': 10966, 'group_order': 960, 'image': None, 'image_isoclass': '960.10966', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 1, 'label': '960.10966.8b4', 'nt': [80, 4], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [8, 1], [4, 2], [4, -2]], [[-4, 2], [-4, -2]], [[4, 2], [-4, -2]], [[-4, 0], [-8, 1], [-4, 2], [-4, -2]], [[-4, 2], [4, -2]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 112595281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 960, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '960.10966.1.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': '960.10966', 'subgroup_hash': 10966, 'subgroup_order': 960, 'subgroup_tex': '\\GL(2,3):D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 112595392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.1040', 'subgroup_hash': 1040, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,3).D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 112595503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 480, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.1017', 'subgroup_hash': 1017, 'subgroup_order': 480, 'subgroup_tex': 'C_{10}\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.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': '480.1029', 'subgroup_hash': 1029, 'subgroup_order': 480, 'subgroup_tex': 'Q_8.D_{30}', 'supersolvable': False, 'sylow': 0}
  • id: 112595530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.974', 'subgroup_hash': 974, 'subgroup_order': 480, 'subgroup_tex': 'D_5\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.972', 'subgroup_hash': 972, 'subgroup_order': 480, 'subgroup_tex': '\\GL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 112595552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.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': '480.968', 'subgroup_hash': 968, 'subgroup_order': 480, 'subgroup_tex': '\\GL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 112595563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 480, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.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': '480.970', 'subgroup_hash': 970, 'subgroup_order': 480, 'subgroup_tex': '\\GL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 112595574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 160, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '960.10966.3.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': '320.1434', 'subgroup_hash': 1434, 'subgroup_order': 320, 'subgroup_tex': 'D_{40}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 240, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.153', 'subgroup_hash': 153, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.109', 'subgroup_hash': 109, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 240, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], '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: 112595315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 240, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.103', 'subgroup_hash': 103, 'subgroup_order': 240, 'subgroup_tex': 'C_5\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 112595337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.106', 'subgroup_hash': 106, 'subgroup_order': 240, 'subgroup_tex': 'C_5:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.105', 'subgroup_hash': 105, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 112595359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.4.h1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '240.150', 'subgroup_hash': 150, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '960.10966.5.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': '192.1485', 'subgroup_hash': 1485, 'subgroup_order': 192, 'subgroup_tex': '\\GL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 112595381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 160, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.6.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': '160.222', 'subgroup_hash': 222, 'subgroup_order': 160, 'subgroup_tex': 'Q_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.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': '160.219', 'subgroup_hash': 219, 'subgroup_order': 160, 'subgroup_tex': 'D_4:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.122', 'subgroup_hash': 122, 'subgroup_order': 160, 'subgroup_tex': 'C_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.153', 'subgroup_hash': 153, 'subgroup_order': 160, 'subgroup_tex': 'D_{20}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 80, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.194', 'subgroup_hash': 194, 'subgroup_order': 160, 'subgroup_tex': 'C_{10}\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.125', 'subgroup_hash': 125, 'subgroup_order': 160, 'subgroup_tex': 'D_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.163', 'subgroup_hash': 163, 'subgroup_order': 160, 'subgroup_tex': 'C_{20}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '160.135', 'subgroup_hash': 135, 'subgroup_order': 160, 'subgroup_tex': 'C_8:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '160.134', 'subgroup_hash': 134, 'subgroup_order': 160, 'subgroup_tex': 'D_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.137', 'subgroup_hash': 137, 'subgroup_order': 160, 'subgroup_tex': 'C_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.136', 'subgroup_hash': 136, 'subgroup_order': 160, 'subgroup_tex': 'C_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.136', 'subgroup_hash': 136, 'subgroup_order': 160, 'subgroup_tex': 'C_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.137', 'subgroup_hash': 137, 'subgroup_order': 160, 'subgroup_tex': 'C_8.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.134', 'subgroup_hash': 134, 'subgroup_order': 160, 'subgroup_tex': 'D_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 80, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '160.135', 'subgroup_hash': 135, 'subgroup_order': 160, 'subgroup_tex': 'C_8:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 120, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, '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: 112595514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 40, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.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': '120.20', 'subgroup_hash': 20, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.30', 'subgroup_hash': 30, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '120.11', 'subgroup_hash': 11, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '120.9', 'subgroup_hash': 9, 'subgroup_order': 120, 'subgroup_tex': 'C_6.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '120.13', 'subgroup_hash': 13, 'subgroup_order': 120, 'subgroup_tex': 'C_5:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112595522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.10.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': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.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': '96.202', 'subgroup_hash': 202, 'subgroup_order': 96, 'subgroup_tex': 'D_4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 112595524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.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': '96.190', 'subgroup_hash': 190, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 112595525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 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': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 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': '96.190', 'subgroup_hash': 190, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 112595527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 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': '96.192', 'subgroup_hash': 192, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 112595528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.10.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 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': '96.193', 'subgroup_hash': 193, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 112595529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 80, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.47', 'subgroup_hash': 47, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 80, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.41', 'subgroup_hash': 41, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 80, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.44', 'subgroup_hash': 44, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '80.38', 'subgroup_hash': 38, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.44', 'subgroup_hash': 44, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.38', 'subgroup_hash': 38, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.38', 'subgroup_hash': 38, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.23', 'subgroup_hash': 23, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 112595540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.10', 'subgroup_hash': 10, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.40', 'subgroup_hash': 40, 'subgroup_order': 80, 'subgroup_tex': 'D_4:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.5', 'subgroup_hash': 5, 'subgroup_order': 80, 'subgroup_tex': 'C_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.40', 'subgroup_hash': 40, 'subgroup_order': 80, 'subgroup_tex': 'D_4:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.40', 'subgroup_hash': 40, 'subgroup_order': 80, 'subgroup_tex': 'D_4:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.15', 'subgroup_hash': 15, 'subgroup_order': 80, 'subgroup_tex': 'C_5:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.16', 'subgroup_hash': 16, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 40, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.15', 'subgroup_hash': 15, 'subgroup_order': 80, 'subgroup_tex': 'C_5:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.16', 'subgroup_hash': 16, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 40, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.26', 'subgroup_hash': 26, 'subgroup_order': 80, 'subgroup_tex': 'C_5\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.41', 'subgroup_hash': 41, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.5', 'subgroup_hash': 5, 'subgroup_order': 80, 'subgroup_tex': 'C_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.7', 'subgroup_hash': 7, 'subgroup_order': 80, 'subgroup_tex': 'D_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 112595565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.6', 'subgroup_hash': 6, 'subgroup_order': 80, 'subgroup_tex': 'C_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.17', 'subgroup_hash': 17, 'subgroup_order': 80, 'subgroup_tex': 'Q_8:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.6', 'subgroup_hash': 6, 'subgroup_order': 80, 'subgroup_tex': 'C_{40}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.17', 'subgroup_hash': 17, 'subgroup_order': 80, 'subgroup_tex': 'Q_8:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.18', 'subgroup_hash': 18, 'subgroup_order': 80, 'subgroup_tex': 'C_5:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.8', 'subgroup_hash': 8, 'subgroup_order': 80, 'subgroup_tex': 'C_5:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.18', 'subgroup_hash': 18, 'subgroup_order': 80, 'subgroup_tex': 'C_5:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '960.10966.15.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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 112595573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 20, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112595575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 20, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112595579
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 20, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112595580
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.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': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.16.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.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': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 48, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.20.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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 48, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 48, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 112595289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.20.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '48.28', 'subgroup_hash': 28, 'subgroup_order': 48, 'subgroup_tex': 'C_2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 112595291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 40, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 40, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 112595294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 20, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.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': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.4', 'subgroup_hash': 4, 'subgroup_order': 40, 'subgroup_tex': 'C_5:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.4', 'subgroup_hash': 4, 'subgroup_order': 40, 'subgroup_tex': 'C_5:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.4', 'subgroup_hash': 4, 'subgroup_order': 40, 'subgroup_tex': 'C_5:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595322
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 112595323
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 137, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 112595324
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595325
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112595330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.30.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595343
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.32.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112595344
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 156, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112595345
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 112595346
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112595347
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.32.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.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': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112595349
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112595350
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112595351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 24, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 112595352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112595358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112595360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 20, 'counter': 170, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.48.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': [], 'split': False, '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: 112595361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 20, 'counter': 171, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595362
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 20, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.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': [], '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: 112595363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595364
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595367
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595368
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112595369
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595371
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112595375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 16, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 8, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112595412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.60.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 112595419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '960.10966.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 112595420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595425
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112595427
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.h1.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.80.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.i1.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112595432
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 10, 'counter': 235, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10966.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C5'], '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: 112595433
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 5, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595434
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 5, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595435
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595436
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595438
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 5, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595439
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 112595440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 8, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112595443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112595447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112595457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.120.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.120.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595472
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.120.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595473
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.120.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595474
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.120.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 112595475
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 112595476
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 112595477
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 112595478
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 112595479
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.160.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.d1.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': 160, 'quotient_simple': 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: 112595480
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 112595482
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.160.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 112595483
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 5, 'counter': 281, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '960.10966.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1485', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1485, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['C6'], '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: 112595484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10966.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': 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': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 112595488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595490
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595491
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595493
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595494
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595495
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 292, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112595496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10966.240.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112595499
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '960.10966.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, '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: 112595500
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 297, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10966.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.1193', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1193, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_{10}\\times S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1', '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: 112595501
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595502
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595505
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595506
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595507
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595508
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10966.480.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112595509
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10966', 'ambient_counter': 10966, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 1, 'counter': 304, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '960.10966.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '960.10966', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10966, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 960, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):D_{10}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D4', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 112595502
    {'ambient': '960.10966', 'aut_centralizer_order': 384, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '10.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '160.c1.a1', '240.b1.a1', '240.m1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [452, -1, 9927, -1, 1792, -1, 1539, -1], 'generators': [12], 'label': '960.10966.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1.a1', 'old_label': '480.c1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595281
    {'ambient': '960.10966', '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': '480.a1.a1', 'complements': ['960.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '4.h1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4938, 4448, 5296, 5328, 2179, 4887, 2664, 4644], 'generators': [1, 192, 240, 12, 264, 480, 2, 8], 'label': '960.10966.1.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', '2.e1.a1', '2.d1.a1', '2.g1.a1', '2.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '480.1193', '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': '480.1193'}
  • id: 112595282
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': ['240.m1.a1', '240.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '16.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4814, 7802, 4863, 1717, 1424, 4344, 2014, 4644], 'generators': [2, 480, 192, 504, 8, 240], 'label': '960.10966.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '480.1193', '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: 112595283
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': ['48.m1.a1', '48.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '60.a1.a1', '80.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4747, 7172, 4829, 2797, 2325, 5707, 2956, 5756], 'generators': [2, 480, 8, 744, 240], 'label': '960.10966.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '480.1193', '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': '48.48'}
  • id: 112595284
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '20.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '24.a1.a1', 'complements': ['48.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1', '10.d1.a1', '10.f1.a1'], 'contains': ['40.a1.a1', '60.v1.a1', '80.c1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5223, 8316, 5161, 4481, 2712, 6775, 2738, 6775], 'generators': [1, 480, 8, 264, 240], 'label': '960.10966.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.c1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 112595285
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '20.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': ['48.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.a1.a1', '10.e1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '60.ba1.a1', '80.d1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4989, 8992, 4714, 3856, 2945, 8087, 2657, 8087], 'generators': [3, 480, 8, 264, 240], 'label': '960.10966.20.c1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.c1.a1', 'normal_contained_in': ['4.d1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595286
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.51', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '5.a1.a1'], 'contains': ['40.b1.a1', '40.c1.a1', '40.d1.a1', '40.e1.a1', '40.f1.a1', '40.g1.a1', '40.h1.a1', '60.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1741, -1, 8104, -1, 1723, -1, 1593, -1], 'generators': [1, 8, 2, 12, 480], 'label': '960.10966.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '20.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112595287
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.b1.a1', '10.d1.a1', '10.e1.a1'], 'contains': ['40.a1.a1', '60.p1.a1', '80.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5106, -1, 5593, -1, 2125, -1, 3255, -1], 'generators': [12, 480, 8, 744, 240], 'label': '960.10966.20.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595288
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.b1.a1', '10.f1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '60.bg1.a1', '80.f1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4511, -1, 5277, -1, 2811, -1, 3105, -1], 'generators': [14, 480, 8, 744, 240], 'label': '960.10966.20.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595289
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.c1.a1', '10.d1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '60.bj1.a1', '80.e1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4599, -1, 5420, -1, 2540, -1, 2819, -1], 'generators': [5, 480, 8, 744, 240], 'label': '960.10966.20.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595290
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '10.c1.a1', '10.e1.a1', '10.f1.a1'], 'contains': ['40.a1.a1', '60.bm1.a1', '80.g1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4865, -1, 5002, -1, 2626, -1, 3393, -1], 'generators': [7, 480, 8, 744, 240], 'label': '960.10966.20.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595291
    {'ambient': '960.10966', 'aut_centralizer_order': 48, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '20.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '120.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1856, 2291, 8060, 8049, 2800, 1819, 2883, 1675], 'generators': [2, 480, 192, 12], 'label': '960.10966.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '480.1193', '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: 112595292
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.w1.a1', '12.bb1.a1', '12.bj1.a1', '12.bm1.a1'], 'contains': ['48.i1.a1', '120.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7530, 3565, 2355, 6841, 5985, 2775, 5060, 2644], 'generators': [504, 192, 480, 240], 'label': '960.10966.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['96.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '480.1193', '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': '48.48'}
  • id: 112595293
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['240.l1.a1', '240.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '16.b1.a1', '20.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5336, 2298, 5683, 9144, 1175, 1475, 2590, 2213], 'generators': [12, 480, 504, 240, 8, 192], 'label': '960.10966.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.e1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595294
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '48.l1.a1', '120.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1689, -1, 7746, -1, 2668, -1, 2611, -1], 'generators': [1, 480, 192, 2], 'label': '960.10966.24.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595295
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '60.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.j1.a1', '120.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3922, -1, 5913, -1, 4629, -1, 4720, -1], 'generators': [2, 480, 192, 516], 'label': '960.10966.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '480.1193', '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: 112595296
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1', '12.f1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.k1.a1', '120.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2081, -1, 7423, -1, 2888, -1, 3179, -1], 'generators': [5, 480, 192, 2], 'label': '960.10966.24.e1.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.e1.a1', 'projective_image': '480.1193', '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': '20.4'}
  • id: 112595297
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.e1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.i1.a1', '120.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5722, -1, 4281, -1, 4839, -1, 4922, -1], 'generators': [2, 192, 480, 504], 'label': '960.10966.24.f1.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.f1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595298
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.d1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.g1.a1', '48.m1.a1', '120.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1286, -1, 8865, -1, 2505, -1, 2768, -1], 'generators': [1, 480, 192, 12], 'label': '960.10966.24.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595299
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.l1.a1', '12.n1.a1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.k1.a1', '120.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2645, -1, 7234, -1, 3064, -1, 3263, -1], 'generators': [3, 480, 192, 12], 'label': '960.10966.24.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595300
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.l1.a1', '12.o1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.h1.a1', '120.i1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4018, -1, 5785, -1, 4542, -1, 4636, -1], 'generators': [506, 480, 192, 12], 'label': '960.10966.24.i1.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.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595301
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.m1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.b1.a1', '48.i1.a1', '48.j1.a1', '120.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5462, -1, 4166, -1, 5199, -1, 5519, -1], 'generators': [12, 480, 192, 504], 'label': '960.10966.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595302
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.l1.a1', '12.r1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.h1.a1', '120.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3138, -1, 6653, -1, 3792, -1, 3601, -1], 'generators': [1, 192, 480, 266], 'label': '960.10966.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595303
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.a1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.k1.a1', '120.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3296, -1, 6265, -1, 3595, -1, 3852, -1], 'generators': [1, 480, 192, 278], 'label': '960.10966.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595304
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': ['240.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '12.w1.a1', '16.c1.a1', '20.b1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5560, 4816, 5153, 3302, 1982, 6775, 2254, 6775], 'generators': [1, 480, 8, 264, 192, 240], 'label': '960.10966.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595305
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.m1.a1', '12.r1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.j1.a1', '120.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 7019, -1, 3683, -1, 3937, -1], 'generators': [1, 480, 192, 276], 'label': '960.10966.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595306
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.d1.a1', '12.r1.a1', '12.s1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.k1.a1', '120.n1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2989, -1, 6919, -1, 3188, -1, 3383, -1], 'generators': [1, 480, 192, 14], 'label': '960.10966.24.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595307
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 120, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.s1.a1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1'], 'contains': ['48.d1.a1', '48.i1.a1', '120.o1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5354, -1, 3856, -1, 5461, -1, 5186, -1], 'generators': [1, 192, 480, 264], 'label': '960.10966.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595308
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.a1', '12.x1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.g1.a1', '48.n1.a1', '120.p1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2521, -1, 6766, -1, 3475, -1, 3737, -1], 'generators': [5, 480, 192, 254], 'label': '960.10966.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595309
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.d1.a1', '12.r1.a1', '12.x1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.g1.a1', '120.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2858, -1, 7494, -1, 2976, -1, 2968, -1], 'generators': [5, 480, 192, 14], 'label': '960.10966.24.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595310
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.n1.a1', '12.r1.a1'], 'contains': ['48.e1.a1', '48.j1.a1', '48.k1.a1', '120.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3407, -1, 6469, -1, 4069, -1, 4433, -1], 'generators': [3, 480, 192, 276], 'label': '960.10966.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.r1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595311
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 120, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.n1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1'], 'contains': ['48.e1.a1', '48.i1.a1', '120.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6181, -1, 3652, -1, 5330, -1, 5645, -1], 'generators': [3, 192, 480, 264], 'label': '960.10966.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.s1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595312
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.o1.a1', '12.bc1.a1'], 'contains': ['48.f1.a1', '48.h1.a1', '48.j1.a1', '120.t1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5139, -1, 4860, -1, 5854, -1, 6489, -1], 'generators': [242, 480, 192, 516], 'label': '960.10966.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.t1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595313
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.s1.a1', '12.x1.a1', '12.bc1.a1', '12.bd1.a1', '12.be1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.i1.a1', '120.u1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5247, -1, 4395, -1, 4983, -1, 5393, -1], 'generators': [14, 480, 192, 504], 'label': '960.10966.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.u1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595314
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 24, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.h1.a1', '12.o1.a1', '12.t1.a1', '12.y1.a1', '12.bf1.a1', '12.bg1.a1'], 'contains': ['48.f1.a1', '48.i1.a1', '120.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7044, -1, 3566, -1, 6665, -1, 6678, -1], 'generators': [254, 480, 192, 504], 'label': '960.10966.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.v1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595315
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': ['240.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.bb1.a1', '16.d1.a1', '20.c1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5141, 9513, 4605, 5633, 2295, 8087, 1657, 8087], 'generators': [3, 480, 8, 264, 192, 240], 'label': '960.10966.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595316
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.l1.a1', '12.r1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.k1.a1', '120.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3526, -1, 6352, -1, 3923, -1, 4042, -1], 'generators': [5, 480, 192, 242], 'label': '960.10966.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.w1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595317
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 24, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.x1.a1', '12.bf1.a1', '12.bh1.a1', '12.bi1.a1', '12.bj1.a1'], 'contains': ['48.g1.a1', '48.i1.a1', '120.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5550, -1, 4773, -1, 5091, -1, 5289, -1], 'generators': [5, 480, 192, 240], 'label': '960.10966.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.x1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595318
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.r1.a1', '12.bc1.a1'], 'contains': ['48.c1.a1', '48.h1.a1', '48.j1.a1', '120.y1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3833, -1, 5983, -1, 4717, -1, 4804, -1], 'generators': [506, 480, 192, 516], 'label': '960.10966.24.y1.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.y1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595319
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 120, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.o1.a1', '12.u1.a1', '12.z1.a1', '12.bc1.a1', '12.bh1.a1', '12.bk1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '120.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7133, -1, 2477, -1, 6773, -1, 6782, -1], 'generators': [242, 192, 480, 504], 'label': '960.10966.24.z1.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.z1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595320
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 24, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.h1.a1', '12.v1.a1', '12.ba1.a1', '12.bc1.a1', '12.bi1.a1', '12.bl1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '120.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6091, -1, 3740, -1, 6883, -1, 6887, -1], 'generators': [252, 480, 192, 504], 'label': '960.10966.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595321
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 24, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.n1.a1', '12.s1.a1', '12.bg1.a1', '12.bk1.a1', '12.bl1.a1', '12.bm1.a1'], 'contains': ['48.i1.a1', '48.k1.a1', '120.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5621, -1, 3466, -1, 6095, -1, 5750, -1], 'generators': [7, 480, 192, 240], 'label': '960.10966.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595322
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.p1.a1', '12.w1.a1', '12.z1.a1', '12.bd1.a1', '12.bg1.a1', '12.bi1.a1'], 'contains': ['48.i1.a1', '120.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9669, -1, 945, -1, 7057, -1, 7051, -1], 'generators': [241, 264, 480, 192], 'label': '960.10966.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595323
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.q1.a1', '12.u1.a1', '12.bb1.a1', '12.be1.a1', '12.bf1.a1', '12.bl1.a1'], 'contains': ['48.i1.a1', '120.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9032, -1, 382, -1, 7229, -1, 6970, -1], 'generators': [243, 264, 480, 192], 'label': '960.10966.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595324
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.q1.a1', '12.t1.a1', '12.ba1.a1', '12.bd1.a1', '12.bh1.a1', '12.bm1.a1'], 'contains': ['48.i1.a1', '120.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7939, -1, 712, -1, 6971, -1, 7218, -1], 'generators': [511, 480, 192, 240], 'label': '960.10966.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595325
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.p1.a1', '12.v1.a1', '12.y1.a1', '12.be1.a1', '12.bj1.a1', '12.bk1.a1'], 'contains': ['48.i1.a1', '120.bf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9370, -1, 1119, -1, 7143, -1, 7134, -1], 'generators': [509, 480, 192, 720], 'label': '960.10966.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bf1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595326
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['240.m1.a1', '240.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '16.f1.a1', '20.f1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4345, 1040, 5308, 7979, 2139, 2500, 2439, 1188], 'generators': [14, 480, 504, 240, 8, 192], 'label': '960.10966.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.g1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595327
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.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', '60.j1.a1', '60.k1.a1', '60.l1.a1', '60.q1.a1', '60.r1.a1', '60.w1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4757, -1, 5045, -1, 4405, -1, 4644, -1], 'generators': [1, 2, 12, 264], 'label': '960.10966.30.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': '480.1193', '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': '32.46'}
  • id: 112595328
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.14', 'aut_weyl_index': 240, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.h1.a1', '60.i1.a1', '60.n1.a1', '60.o1.a1', '60.bc1.a1', '60.bd1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9953, -1, 44, -1, 9801, -1, 9948, -1], 'generators': [241, 2, 12], 'label': '960.10966.30.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': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595329
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.f1.a1', '60.m1.a1', '60.p1.a1', '60.bb1.a1', '60.bg1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6417, -1, 3402, -1, 8214, -1, 8304, -1], 'generators': [2, 12, 504, 240], 'label': '960.10966.30.c1.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.c1.a1', 'projective_image': '480.1193', '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': '96.226'}
  • id: 112595330
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '60.f1.a1', '60.i1.a1', '60.s1.a1', '60.u1.a1', '60.x1.a1', '60.z1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6989, -1, 2864, -1, 9507, -1, 9836, -1], 'generators': [1, 2, 252], 'label': '960.10966.30.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': '480.1193', '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': '32.46'}
  • id: 112595331
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.e1.a1', '60.h1.a1', '60.t1.a1', '60.v1.a1', '60.y1.a1', '60.ba1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8533, -1, 564, -1, 9029, -1, 8458, -1], 'generators': [1, 2, 240], 'label': '960.10966.30.e1.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.e1.a1', 'projective_image': '480.1193', '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: 112595332
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '240.g1.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', '60.be1.a1', '60.bf1.a1', '60.bi1.a1', '60.bl1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7879, -1, 2602, -1, 9694, -1, 9232, -1], 'generators': [241, 2, 252], 'label': '960.10966.30.f1.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.f1.a1', 'projective_image': '480.1193', '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': '16.11'}
  • id: 112595333
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.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', '60.bh1.a1', '60.bj1.a1', '60.bk1.a1', '60.bm1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8364, -1, 701, -1, 8329, -1, 9011, -1], 'generators': [5, 2, 504], 'label': '960.10966.30.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': '480.1193', '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': '32.46'}
  • id: 112595334
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '15.a1.a1'], 'contains': ['60.k1.a1', '60.m1.a1', '60.o1.a1', '60.s1.a1', '60.t1.a1', '60.be1.a1', '60.bh1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8239, -1, 1771, -1, 9400, -1, 9411, -1], 'generators': [1, 242, 12], 'label': '960.10966.30.h1.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.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 112595335
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.k1.a1', '60.n1.a1', '60.p1.a1', '60.u1.a1', '60.v1.a1', '60.bi1.a1', '60.bj1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7490, -1, 3024, -1, 8694, -1, 8850, -1], 'generators': [1, 12, 240], 'label': '960.10966.30.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595336
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '240.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '15.a1.a1'], 'contains': ['60.l1.a1', '60.m1.a1', '60.n1.a1', '60.x1.a1', '60.y1.a1', '60.bf1.a1', '60.bk1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8715, -1, 1052, -1, 9606, -1, 9316, -1], 'generators': [241, 242, 12], 'label': '960.10966.30.j1.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.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595372
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.h1.a2', '24.c1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.e1.a1', '240.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [572, -1, 8722, -1, 2062, -1, 1076, -1], 'generators': [1, 192, 2], 'label': '960.10966.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '48.l1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595337
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['240.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.bj1.a1', '16.e1.a1', '20.g1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4656, 6258, 5511, 6969, 1653, 5600, 1830, 3388], 'generators': [5, 480, 192, 744, 8, 240], 'label': '960.10966.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595338
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '10.e1.a1', '15.a1.a1'], 'contains': ['60.l1.a1', '60.o1.a1', '60.p1.a1', '60.z1.a1', '60.ba1.a1', '60.bl1.a1', '60.bm1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7083, -1, 1922, -1, 8862, -1, 9130, -1], 'generators': [3, 12, 240], 'label': '960.10966.30.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 112595339
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '15.a1.a1'], 'contains': ['60.r1.a1', '60.t1.a1', '60.u1.a1', '60.bb1.a1', '60.bd1.a1', '60.bk1.a1', '60.bl1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7232, -1, 2021, -1, 9925, -1, 9522, -1], 'generators': [1, 242, 252], 'label': '960.10966.30.l1.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.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 112595340
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '10.f1.a1', '15.a1.a1'], 'contains': ['60.r1.a1', '60.s1.a1', '60.v1.a1', '60.bc1.a1', '60.bf1.a1', '60.bg1.a1', '60.bm1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9350, -1, 1585, -1, 8436, -1, 8706, -1], 'generators': [1, 14, 240], 'label': '960.10966.30.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595341
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '15.a1.a1'], 'contains': ['60.w1.a1', '60.y1.a1', '60.z1.a1', '60.bb1.a1', '60.bc1.a1', '60.bh1.a1', '60.bi1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7666, -1, 2253, -1, 9240, -1, 9683, -1], 'generators': [241, 242, 252], 'label': '960.10966.30.n1.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.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595342
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '30.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.46', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1', '10.g1.a1', '15.a1.a1'], 'contains': ['60.w1.a1', '60.x1.a1', '60.ba1.a1', '60.bd1.a1', '60.be1.a1', '60.bg1.a1', '60.bj1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9081, -1, 1410, -1, 8535, -1, 8611, -1], 'generators': [5, 14, 504], 'label': '960.10966.30.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 112595343
    {'ambient': '960.10966', 'aut_centralizer_order': 120, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '160.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [792, -1, 8640, -1, 1475, -1, 1806, -1], 'generators': [480, 192, 8], 'label': '960.10966.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.a1.a1', 'projective_image': '480.1193', '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: 112595344
    {'ambient': '960.10966', 'aut_centralizer_order': 60, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.h1.a2'], 'contains': ['64.a1.a1', '96.b1.a1', '160.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [141, -1, 9232, -1, 1021, -1, 588, -1], 'generators': [2, 192, 8], 'label': '960.10966.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.b1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595345
    {'ambient': '960.10966', 'aut_centralizer_order': 12, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.i1.a1', '16.i1.a2'], 'contains': ['64.a1.a1', '96.c1.a1', '160.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [47, -1, 9849, -1, 714, -1, 1280, -1], 'generators': [12, 192, 8], 'label': '960.10966.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.c1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 112595346
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.5', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '160.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [299, -1, 9536, -1, 914, -1, 939, -1], 'generators': [1, 8, 192], 'label': '960.10966.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595347
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.5', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.h1.a2', '16.i1.a2'], 'contains': ['64.a1.a1', '96.d1.a1', '160.d1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [299, -1, 9640, -1, 914, -1, 815, -1], 'generators': [481, 8, 192], 'label': '960.10966.32.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595348
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['240.m1.a1', '240.l1.a1', '240.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '12.bm1.a1', '16.g1.a1', '20.h1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5013, 3557, 5027, 4467, 1825, 3238, 3104, 5750], 'generators': [7, 480, 192, 744, 8, 240], 'label': '960.10966.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595349
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.5', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.h1.a1', '16.h1.a2'], 'contains': ['64.a1.a1', '96.e1.a1', '160.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [465, -1, 9048, -1, 1283, -1, 691, -1], 'generators': [3, 8, 192], 'label': '960.10966.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.e1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595350
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '120.36', 'aut_weyl_index': 32, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.i1.a1', '16.i1.a2'], 'contains': ['64.a1.a1', '96.g1.a1', '160.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [211, -1, 9725, -1, 1106, -1, 1451, -1], 'generators': [5, 192, 8], 'label': '960.10966.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.f1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 112595351
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '40.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 160, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1', '20.e1.a1', '20.f1.a1', '20.g1.a1', '20.h1.a1'], 'contains': ['120.a1.a1', '160.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5190, 7172, 4564, 4481, 2279, 5707, 3498, 5756], 'generators': [8, 744, 240, 480], 'label': '960.10966.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 40, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1', '20.c1.a1', '20.b1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '480.1193', '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': '24.12'}
  • id: 112595352
    {'ambient': '960.10966', 'aut_centralizer_order': 24, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '10.b1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.f1.a1', '120.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1457, -1, 8206, -1, 1635, -1, 1697, -1], 'generators': [2, 12, 8, 480], 'label': '960.10966.40.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.b1.a1', 'projective_image': '480.1193', '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': '8.5'}
  • id: 112595353
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '10.a1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '80.d1.a1', '80.h1.a1', '80.h1.a2', '120.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1014, -1, 8562, -1, 1184, -1, 611, -1], 'generators': [1, 2, 480, 8], 'label': '960.10966.40.c1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '40.c1.a1', 'projective_image': '480.1193', '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': '12.4'}
  • id: 112595354
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '10.c1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.e1.a1', '80.g1.a1', '120.e1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1577, -1, 7914, -1, 1817, -1, 1956, -1], 'generators': [5, 2, 480, 8], 'label': '960.10966.40.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112595355
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '10.d1.a1', '20.d1.a1'], 'contains': ['80.b1.a1', '80.c1.a1', '80.e1.a1', '80.i1.a1', '80.i1.a2', '120.g1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [742, -1, 9320, -1, 1034, -1, 1202, -1], 'generators': [1, 12, 480, 8], 'label': '960.10966.40.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595356
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '10.e1.a1', '20.d1.a1'], 'contains': ['80.b1.a1', '80.d1.a1', '80.g1.a1', '120.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2096, -1, 7408, -1, 1991, -1, 2041, -1], 'generators': [3, 12, 480, 8], 'label': '960.10966.40.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112595357
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '10.f1.a1', '20.d1.a1'], 'contains': ['80.c1.a1', '80.f1.a1', '80.g1.a1', '120.n1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3271, -1, 6972, -1, 2100, -1, 2145, -1], 'generators': [1, 14, 480, 8], 'label': '960.10966.40.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595358
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 160, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '10.g1.a1', '20.d1.a1'], 'contains': ['80.d1.a1', '80.e1.a1', '80.f1.a1', '120.q1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2377, -1, 8292, -1, 1904, -1, 1594, -1], 'generators': [5, 14, 480, 8], 'label': '960.10966.40.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112595359
    {'ambient': '960.10966', 'aut_centralizer_order': 1, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '960.11377', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '12.d1.a1', '20.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1676, -1, 8046, -1, 995, -1, 1449, -1], 'generators': [1, 192, 12, 480, 2, 8], 'label': '960.10966.4.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '4.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595360
    {'ambient': '960.10966', 'aut_centralizer_order': 480, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2093, 3957, 7708, 6457, 2668, 3263, 2625, 3125], 'generators': [2, 192, 480], 'label': '960.10966.48.a1.a1', 'mobius_quo': 0, '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': '480.1193', '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: 112595361
    {'ambient': '960.10966', 'aut_centralizer_order': 96, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '20.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '240.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1329, 2691, 8965, 8284, 2548, 1656, 2967, 2094], 'generators': [12, 192, 480], 'label': '960.10966.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '480.1193', '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': '20.4'}
  • id: 112595362
    {'ambient': '960.10966', 'aut_centralizer_order': 96, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '20.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.a1.a1', '24.n1.a1', '24.q1.a1', '24.u1.a1', '24.y1.a1'], 'contains': ['96.a1.a1', '240.i1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3520, 1992, 7243, 7638, 3430, 2225, 3541, 1525], 'generators': [14, 192, 480], 'label': '960.10966.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.c1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '480.1193', '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': '20.4'}
  • id: 112595363
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.c1.a1', '24.g1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '240.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1744, -1, 7524, -1, 2824, -1, 2851, -1], 'generators': [1, 192, 480], 'label': '960.10966.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595364
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.c1.a1', '24.h1.a1', '24.k1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '240.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2715, -1, 7340, -1, 3065, -1, 3260, -1], 'generators': [3, 192, 480], 'label': '960.10966.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595365
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '60.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.i1.a1', '24.l1.a1', '24.p1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '240.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4270, -1, 5577, -1, 4555, -1, 4556, -1], 'generators': [518, 192, 480], 'label': '960.10966.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 112595366
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '120.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.e1.a1', '24.g1.a1', '24.m1.a1', '24.p1.a1', '24.q1.a1', '24.w1.a1', '24.x1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '240.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2401, -1, 7804, -1, 2945, -1, 3457, -1], 'generators': [5, 192, 480], 'label': '960.10966.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 112595367
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.i1.a1', '24.k1.a1', '24.t1.a1', '24.w1.a1', '24.y1.a1', '24.z1.a1'], 'contains': ['96.a1.a1', '240.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4071, -1, 5800, -1, 4640, -1, 4637, -1], 'generators': [506, 480, 192], 'label': '960.10966.48.h1.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': '48.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595368
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.f1.a1', '24.j1.a1', '24.o1.a1', '24.s1.a1', '24.u1.a1', '24.v1.a1', '24.x1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.be1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '240.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5717, -1, 4027, -1, 6095, -1, 5750, -1], 'generators': [504, 480, 192], 'label': '960.10966.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595369
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '60.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.j1.a1', '24.m1.a1', '24.r1.a1', '24.t1.a1', '24.y1.a1', '24.ba1.a1'], 'contains': ['96.a1.a1', '240.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3922, -1, 5945, -1, 4727, -1, 4720, -1], 'generators': [516, 192, 480], 'label': '960.10966.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 112595370
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 20, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '10.d1.a1', '10.e1.a1', '10.f1.a1', '10.g1.a1', '15.a1.a1', '20.d1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4839, -1, 5326, -1, 2814, -1, 3331, -1], 'generators': [1, 240, 264, 2, 480, 12, 8], 'label': '960.10966.5.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': '480.1193', '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': '96.226'}
  • id: 112595371
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 96, 'centralizer': '120.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.e1.a1', '24.h1.a1', '24.l1.a1', '24.n1.a1', '24.r1.a1', '24.w1.a1', '24.bb1.a1'], 'contains': ['96.a1.a1', '240.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2875, -1, 6478, -1, 3587, -1, 3948, -1], 'generators': [7, 192, 480], 'label': '960.10966.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 112595373
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '20.3', 'aut_weyl_index': 192, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.i1.a2', '24.g1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.g1.a1', '240.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [462, -1, 9801, -1, 1390, -1, 1533, -1], 'generators': [1, 192, 12], 'label': '960.10966.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '48.m1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 112595374
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '20.3', 'aut_weyl_index': 192, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1'], 'contains': ['96.e1.a1', '96.f1.a1', '96.g1.a1', '240.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1904, -1, 7041, -1, 3343, -1, 3375, -1], 'generators': [5, 192, 254], 'label': '960.10966.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.p1.a1', 'old_label': '48.n1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 112595375
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': ['16.i1.a1', '16.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.c1.a1', '30.e1.a1', '30.g1.a1'], 'contains': ['120.a1.a1', '120.f1.a1', '120.z1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7298, 5423, 1643, 4844, 7338, 4069, 7324, 3931], 'generators': [2, 504, 240], 'label': '960.10966.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 30, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1', '240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '480.1193', 'quotient_action_image': '12.4', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595376
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.d1.a1', '30.a1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.e1.a1', '120.g1.a1', '120.h1.a1', '120.n1.a1', '120.q1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2650, -1, 7104, -1, 3334, -1, 3073, -1], 'generators': [1, 2, 12], 'label': '960.10966.60.b1.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.b1.a1', 'projective_image': '480.1193', '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': '8.5'}
  • id: 112595377
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.b1.a1', '120.d1.a1', '120.f1.a1', '120.i1.a1', '120.j1.a1', '120.u1.a1', '120.y1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5771, -1, 4535, -1, 6314, -1, 6594, -1], 'generators': [2, 12, 504], 'label': '960.10966.60.c1.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.c1.a1', 'projective_image': '480.1193', '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': '8.5'}
  • id: 112595378
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.a1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.e1.a1', '120.l1.a1', '120.m1.a1', '120.p1.a1', '120.r1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3056, -1, 6108, -1, 4345, -1, 4294, -1], 'generators': [1, 2, 276], 'label': '960.10966.60.d1.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.d1.a1', 'projective_image': '480.1193', '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': '8.5'}
  • id: 112595379
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '30.a1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.c1.a1', '120.f1.a1', '120.k1.a1', '120.o1.a1', '120.s1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4946, -1, 4623, -1, 6205, -1, 5856, -1], 'generators': [1, 2, 264], 'label': '960.10966.60.e1.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.e1.a1', 'projective_image': '480.1193', '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': '16.11'}
  • id: 112595380
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '30.c1.a1', '30.d1.a1', '30.f1.a1'], 'contains': ['120.d1.a1', '120.f1.a1', '120.t1.a1', '120.v1.a1', '120.ba1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6337, -1, 3736, -1, 8122, -1, 8077, -1], 'generators': [2, 252, 504], 'label': '960.10966.60.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': '480.1193', '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': '16.11'}
  • id: 112595381
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['160.d1.a1', '160.d1.a2', '160.f1.a1', '160.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.e1.a1', '12.h1.a1', '12.o1.a1', '12.bc1.a1', '30.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5941, 1300, 3750, 8085, 4879, 381, 5209, 381], 'generators': [2, 192, 504, 240, 12, 480], 'label': '960.10966.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '480.1193', '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': '480.1193'}
  • id: 112595382
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '30.a1.a1', '30.f1.a1', '30.g1.a1'], 'contains': ['120.e1.a1', '120.f1.a1', '120.w1.a1', '120.x1.a1', '120.bb1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5325, -1, 4874, -1, 6402, -1, 6088, -1], 'generators': [5, 2, 240], 'label': '960.10966.60.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': '480.1193', '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': '16.11'}
  • id: 112595383
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '30.b1.a1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.f1.a1', '120.bc1.a1', '120.bd1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9827, -1, 101, -1, 9762, -1, 8644, -1], 'generators': [241, 2], 'label': '960.10966.60.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': '480.1193', '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: 112595384
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '30.b1.a1', '30.d1.a1', '30.g1.a1'], 'contains': ['120.f1.a1', '120.be1.a1', '120.bf1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9197, -1, 992, -1, 9056, -1, 9844, -1], 'generators': [509, 2], 'label': '960.10966.60.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': '480.1193', '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': '8.5'}
  • id: 112595385
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '240.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '30.a1.a1'], 'contains': ['120.g1.a1', '120.h1.a1', '120.i1.a1', '120.k1.a1', '120.l1.a1', '120.p1.a1', '120.w1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3694, -1, 5963, -1, 4214, -1, 4168, -1], 'generators': [1, 266, 12], 'label': '960.10966.60.j1.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.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595386
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '30.a1.a1', '30.h1.a1', '30.i1.a1'], 'contains': ['120.g1.a1', '120.j1.a1', '120.m1.a1', '120.o1.a1', '120.x1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4808, -1, 5067, -1, 5723, -1, 5982, -1], 'generators': [1, 12, 264], 'label': '960.10966.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595387
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '30.a1.a1', '30.j1.a1', '30.k1.a1'], 'contains': ['120.h1.a1', '120.j1.a1', '120.r1.a1', '120.s1.a1', '120.bb1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5631, -1, 4260, -1, 6490, -1, 6383, -1], 'generators': [3, 12, 264], 'label': '960.10966.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595388
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '30.c1.a1', '30.h1.a1', '30.j1.a1'], 'contains': ['120.i1.a1', '120.j1.a1', '120.t1.a1', '120.v1.a1', '120.z1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6547, -1, 3386, -1, 8033, -1, 7992, -1], 'generators': [242, 12, 504], 'label': '960.10966.60.m1.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.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595389
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '60.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '30.b1.a1', '30.i1.a1', '30.j1.a1'], 'contains': ['120.j1.a1', '120.bc1.a1', '120.bf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9620, -1, 826, -1, 9445, -1, 9429, -1], 'generators': [241, 12], 'label': '960.10966.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595390
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '30.b1.a1', '30.h1.a1', '30.k1.a1'], 'contains': ['120.j1.a1', '120.bd1.a1', '120.be1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9412, -1, 451, -1, 9246, -1, 9752, -1], 'generators': [243, 12], 'label': '960.10966.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595391
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.p1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.e1.a1', '30.c1.a1', '30.i1.a1', '30.k1.a1'], 'contains': ['120.a1.a1', '120.j1.a1', '120.ba1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6457, -1, 3474, -1, 7651, -1, 7805, -1], 'generators': [12, 504, 240], 'label': '960.10966.60.p1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.p1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595392
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.d1.a1', '480.g1.a1', '480.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '6.a1.a1', '8.b1.a1', '10.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4396, 441, 5462, 9222, 1412, 1294, 2758, 1138], 'generators': [2, 192, 8, 504, 12, 480, 240], 'label': '960.10966.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '480.1193', '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': '480.1193'}
  • id: 112595393
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.i1.a1', '12.l1.a1', '12.m1.a1', '12.n1.a1', '12.r1.a1', '12.s1.a1', '12.x1.a1', '30.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3824, -1, 6019, -1, 3836, -1, 4123, -1], 'generators': [1, 192, 12, 264, 2, 480], 'label': '960.10966.6.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': '480.1193', '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': '160.217'}
  • id: 112595394
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.q1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '240.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '30.a1.a1'], 'contains': ['120.k1.a1', '120.m1.a1', '120.n1.a1', '120.q1.a1', '120.r1.a1', '120.w1.a1', '120.y1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4001, -1, 5673, -1, 4455, -1, 4553, -1], 'generators': [1, 266, 276], 'label': '960.10966.60.q1.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.q1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595395
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.r1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '30.a1.a1', '30.l1.a1', '30.m1.a1'], 'contains': ['120.l1.a1', '120.n1.a1', '120.o1.a1', '120.u1.a1', '120.bb1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5036, -1, 4804, -1, 6578, -1, 6299, -1], 'generators': [1, 14, 264], 'label': '960.10966.60.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.r1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595396
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.s1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '30.d1.a1', '30.h1.a1', '30.m1.a1'], 'contains': ['120.o1.a1', '120.v1.a1', '120.be1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8578, -1, 2170, -1, 8425, -1, 8896, -1], 'generators': [1, 254], 'label': '960.10966.60.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.s1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595397
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '30.e1.a1', '30.h1.a1', '30.l1.a1'], 'contains': ['120.o1.a1', '120.z1.a1', '120.bd1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7590, -1, 1172, -1, 9556, -1, 8447, -1], 'generators': [1, 242], 'label': '960.10966.60.t1.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.t1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595398
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.u1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '30.d1.a1', '30.i1.a1', '30.l1.a1'], 'contains': ['120.o1.a1', '120.ba1.a1', '120.bf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6789, -1, 3117, -1, 9650, -1, 9230, -1], 'generators': [1, 252], 'label': '960.10966.60.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.u1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595399
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '20.b1.a1', '30.e1.a1', '30.i1.a1', '30.m1.a1'], 'contains': ['120.a1.a1', '120.o1.a1', '120.bc1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8651, -1, 1839, -1, 7849, -1, 7607, -1], 'generators': [1, 240], 'label': '960.10966.60.v1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.v1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595400
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.w1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '30.a1.a1', '30.n1.a1', '30.o1.a1'], 'contains': ['120.p1.a1', '120.q1.a1', '120.s1.a1', '120.u1.a1', '120.x1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5234, -1, 4963, -1, 5592, -1, 6193, -1], 'generators': [5, 14, 240], 'label': '960.10966.60.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.w1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595401
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '30.d1.a1', '30.j1.a1', '30.o1.a1'], 'contains': ['120.s1.a1', '120.v1.a1', '120.bf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9023, -1, 2039, -1, 8906, -1, 8830, -1], 'generators': [509, 518], 'label': '960.10966.60.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.x1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595402
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '30.e1.a1', '30.j1.a1', '30.n1.a1'], 'contains': ['120.s1.a1', '120.z1.a1', '120.bc1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8067, -1, 1097, -1, 8600, -1, 8537, -1], 'generators': [241, 242], 'label': '960.10966.60.y1.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.y1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595403
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.z1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '30.d1.a1', '30.k1.a1', '30.n1.a1'], 'contains': ['120.s1.a1', '120.ba1.a1', '120.be1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6934, -1, 2937, -1, 8506, -1, 9536, -1], 'generators': [3, 252], 'label': '960.10966.60.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.z1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595404
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1638', 'aut_weyl_index': 12, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.j1.a1', '12.k1.a1', '12.p1.a1', '12.q1.a1', '12.bd1.a1', '12.be1.a1', '30.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9045, -1, 595, -1, 7095, -1, 7683, -1], 'generators': [241, 192, 12, 264, 2, 480], 'label': '960.10966.6.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': '480.1193', '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': '40.13'}
  • id: 112595405
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '60.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '20.c1.a1', '30.e1.a1', '30.k1.a1', '30.o1.a1'], 'contains': ['120.a1.a1', '120.s1.a1', '120.bd1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8315, -1, 1323, -1, 7943, -1, 7517, -1], 'generators': [3, 240], 'label': '960.10966.60.ba1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.ba1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595406
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bb1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '30.c1.a1', '30.l1.a1', '30.n1.a1'], 'contains': ['120.t1.a1', '120.u1.a1', '120.y1.a1', '120.z1.a1', '120.ba1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6637, -1, 3298, -1, 8231, -1, 8183, -1], 'generators': [242, 252, 504], 'label': '960.10966.60.bb1.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.bb1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595407
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.bc1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '60.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '30.b1.a1', '30.m1.a1', '30.n1.a1'], 'contains': ['120.u1.a1', '120.bc1.a1', '120.be1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9320, -1, 692, -1, 8806, -1, 9644, -1], 'generators': [241, 14], 'label': '960.10966.60.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bc1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595408
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '60.bd1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 480, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '30.b1.a1', '30.l1.a1', '30.o1.a1'], 'contains': ['120.u1.a1', '120.bd1.a1', '120.bf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9527, -1, 916, -1, 9961, -1, 9320, -1], 'generators': [509, 14], 'label': '960.10966.60.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bd1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112595409
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.be1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '30.f1.a1', '30.h1.a1', '30.o1.a1'], 'contains': ['120.v1.a1', '120.x1.a1', '120.bd1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8724, -1, 2224, -1, 8974, -1, 8279, -1], 'generators': [5, 518], 'label': '960.10966.60.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.be1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595410
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '120.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '30.f1.a1', '30.j1.a1', '30.m1.a1'], 'contains': ['120.v1.a1', '120.bb1.a1', '120.bc1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9089, -1, 2105, -1, 9151, -1, 8357, -1], 'generators': [241, 254], 'label': '960.10966.60.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bf1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595411
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bg1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 80, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.f1.a1', '30.c1.a1', '30.m1.a1', '30.o1.a1'], 'contains': ['120.a1.a1', '120.u1.a1', '120.v1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8237, -1, 2864, -1, 7447, -1, 7430, -1], 'generators': [14, 504, 240], 'label': '960.10966.60.bg1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bg1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595412
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bh1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '30.g1.a1', '30.h1.a1', '30.n1.a1'], 'contains': ['120.x1.a1', '120.z1.a1', '120.be1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7688, -1, 1553, -1, 8344, -1, 9057, -1], 'generators': [5, 506], 'label': '960.10966.60.bh1.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.bh1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595413
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bi1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '120.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '30.f1.a1', '30.i1.a1', '30.n1.a1'], 'contains': ['120.x1.a1', '120.ba1.a1', '120.bc1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7487, -1, 3192, -1, 8694, -1, 8752, -1], 'generators': [241, 252], 'label': '960.10966.60.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bi1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595414
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bj1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '20.g1.a1', '30.g1.a1', '30.i1.a1', '30.o1.a1'], 'contains': ['120.a1.a1', '120.x1.a1', '120.bf1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8151, -1, 1974, -1, 7538, -1, 7697, -1], 'generators': [5, 504], 'label': '960.10966.60.bj1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bj1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595415
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.g1.a1', '12.h1.a1', '12.k1.a1', '12.t1.a1', '12.v1.a1', '12.y1.a1', '12.ba1.a1', '30.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6450, -1, 3416, -1, 6680, -1, 7002, -1], 'generators': [1, 192, 252, 264, 2, 480], 'label': '960.10966.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '480.1193', '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': '160.217'}
  • id: 112595416
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bk1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '30.g1.a1', '30.j1.a1', '30.l1.a1'], 'contains': ['120.z1.a1', '120.bb1.a1', '120.bf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7762, -1, 1251, -1, 9336, -1, 8970, -1], 'generators': [509, 506], 'label': '960.10966.60.bk1.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.bk1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595417
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bl1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '30.f1.a1', '30.k1.a1', '30.l1.a1'], 'contains': ['120.ba1.a1', '120.bb1.a1', '120.bd1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7210, -1, 2312, -1, 9870, -1, 9143, -1], 'generators': [243, 252], 'label': '960.10966.60.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bl1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595418
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '60.bm1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 240, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '20.h1.a1', '30.g1.a1', '30.k1.a1', '30.m1.a1'], 'contains': ['120.a1.a1', '120.bb1.a1', '120.be1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8515, -1, 1730, -1, 7759, -1, 7909, -1], 'generators': [7, 504], 'label': '960.10966.60.bm1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bm1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595419
    {'ambient': '960.10966', 'aut_centralizer_order': 120, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 480, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.a2', '32.e1.a1', '32.f1.a1'], 'contains': ['192.a1.a1', '320.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [234, -1, 9568, -1, 1271, -1, 1155, -1], 'generators': [8, 192], 'label': '960.10966.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.a1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595420
    {'ambient': '960.10966', 'aut_centralizer_order': 240, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '20.a1.a1', '40.b1.a1', '40.c1.a1', '40.d1.a1'], 'contains': ['160.a1.a1', '160.b1.a1', '240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1279, -1, 8023, -1, 1712, -1, 1703, -1], 'generators': [2, 480, 8], 'label': '960.10966.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '80.a1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595421
    {'ambient': '960.10966', 'aut_centralizer_order': 48, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '80.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '20.e1.a1', '40.b1.a1', '40.e1.a1', '40.f1.a1'], 'contains': ['160.a1.a1', '160.c1.a1', '240.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [974, -1, 9240, -1, 1582, -1, 2041, -1], 'generators': [12, 480, 8], 'label': '960.10966.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.b1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595422
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 320, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '20.b1.a1', '40.c1.a1', '40.e1.a1', '40.g1.a1'], 'contains': ['160.a1.a1', '160.d1.a1', '160.d1.a2', '240.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1387, -1, 9121, -1, 1812, -1, 1607, -1], 'generators': [1, 480, 8], 'label': '960.10966.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '80.c1.a1', 'projective_image': '480.1193', '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: 112595423
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 320, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '20.c1.a1', '40.c1.a1', '40.f1.a1', '40.h1.a1'], 'contains': ['160.a1.a1', '160.e1.a1', '240.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1751, -1, 8149, -1, 1949, -1, 1879, -1], 'generators': [3, 480, 8], 'label': '960.10966.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '80.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595424
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 320, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '20.g1.a1', '40.d1.a1', '40.e1.a1', '40.h1.a1'], 'contains': ['160.a1.a1', '160.f1.a1', '240.f1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1091, -1, 8420, -1, 1880, -1, 1945, -1], 'generators': [5, 480, 8], 'label': '960.10966.80.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595425
    {'ambient': '960.10966', 'aut_centralizer_order': 48, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '80.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '20.f1.a1', '40.b1.a1', '40.g1.a1', '40.h1.a1'], 'contains': ['160.a1.a1', '240.i1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3236, -1, 7631, -1, 2183, -1, 2144, -1], 'generators': [14, 8, 480], 'label': '960.10966.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595426
    {'ambient': '960.10966', 'aut_centralizer_order': 10, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2154', 'aut_weyl_index': 30, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.j1.a1', '12.u1.a1', '12.w1.a1', '12.z1.a1', '12.bb1.a1', '30.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8648, -1, 979, -1, 6379, -1, 5388, -1], 'generators': [1, 480, 240, 192, 2, 264], 'label': '960.10966.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595427
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 320, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '20.h1.a1', '40.d1.a1', '40.f1.a1', '40.g1.a1'], 'contains': ['160.a1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2748, -1, 6806, -1, 2269, -1, 2226, -1], 'generators': [7, 480, 8], 'label': '960.10966.80.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595428
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '40.c1.a1'], 'contains': ['160.b1.a1', '160.d1.a1', '160.e1.a1', '240.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [188, -1, 8797, -1, 1184, -1, 514, -1], 'generators': [1, 2, 8], 'label': '960.10966.80.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '80.h1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595429
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a2', '40.c1.a1'], 'contains': ['160.b1.a1', '160.d1.a2', '160.e1.a1', '240.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [188, -1, 8950, -1, 1184, -1, 448, -1], 'generators': [481, 2, 8], 'label': '960.10966.80.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '80.h1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595430
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '40.e1.a1'], 'contains': ['160.c1.a1', '160.d1.a1', '160.f1.a1', '240.m1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [101, -1, 9902, -1, 814, -1, 1377, -1], 'generators': [1, 12, 8], 'label': '960.10966.80.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.e1.a1', 'old_label': '80.i1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595431
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a2', '40.e1.a1'], 'contains': ['160.c1.a1', '160.d1.a2', '160.f1.a1', '240.m1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [101, -1, 9956, -1, 814, -1, 1184, -1], 'generators': [481, 12, 8], 'label': '960.10966.80.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.e1.a1', 'old_label': '80.i1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595432
    {'ambient': '960.10966', 'aut_centralizer_order': 960, 'aut_label': '96.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1'], 'contains': ['192.a1.a1', '480.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2206, 3181, 7471, 7175, 3141, 2681, 3312, 2544], 'generators': [480, 192], 'label': '960.10966.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': -96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.48', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595433
    {'ambient': '960.10966', 'aut_centralizer_order': 480, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.l1.a1'], 'contains': ['192.a1.a1', '480.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [741, -1, 8806, -1, 2026, -1, 1236, -1], 'generators': [2, 192], 'label': '960.10966.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.b1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595434
    {'ambient': '960.10966', 'aut_centralizer_order': 96, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 192, 'centralizer': '20.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.b1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '480.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [459, -1, 9697, -1, 1718, -1, 1598, -1], 'generators': [12, 192], 'label': '960.10966.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '96.c1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 112595435
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.d1.a2', '48.d1.a1', '48.l1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '480.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [523, -1, 9317, -1, 1873, -1, 1317, -1], 'generators': [1, 192], 'label': '960.10966.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.d1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595436
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.e1.a1', '48.l1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '480.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [897, -1, 8564, -1, 2257, -1, 1672, -1], 'generators': [3, 192], 'label': '960.10966.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '96.e1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595437
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.h1.a1', '12.i1.a1', '12.j1.a1', '12.bf1.a1', '12.bg1.a1', '12.bi1.a1', '12.bl1.a1', '30.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7047, -1, 2796, -1, 6940, -1, 6232, -1], 'generators': [241, 192, 252, 264, 2, 480], 'label': '960.10966.6.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': '480.1193', '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: 112595438
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 192, 'centralizer': '60.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '480.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2485, -1, 6966, -1, 3786, -1, 3687, -1], 'generators': [518, 192], 'label': '960.10966.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '96.f1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 112595439
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 192, 'centralizer': '120.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.g1.a1', '48.m1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '480.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [803, -1, 9408, -1, 2181, -1, 1745, -1], 'generators': [5, 192], 'label': '960.10966.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '96.g1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 112595440
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 160, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.a1', '60.a1.a1', '60.p1.a1', '60.v1.a1', '60.ba1.a1', '60.bg1.a1', '60.bj1.a1', '60.bm1.a1'], 'contains': ['240.h1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7651, 5446, 2399, 5605, 6471, 4238, 6879, 4100], 'generators': [504, 240], 'label': '960.10966.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': -120, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.b1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '480.1193', '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': '24.12'}
  • id: 112595441
    {'ambient': '960.10966', 'aut_centralizer_order': 192, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '20.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.b1.a1', '60.b1.a1', '60.c1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.i1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2099, -1, 7640, -1, 3509, -1, 3151, -1], 'generators': [2, 12], 'label': '960.10966.120.b1.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.b1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595442
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.c1.a1', '60.b1.a1', '60.d1.a1', '60.e1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.d1.a1', '240.l1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1973, -1, 7184, -1, 3261, -1, 2738, -1], 'generators': [1, 2, 480], 'label': '960.10966.120.c1.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.c1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595443
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.c1.a1', '60.d1.a1', '60.f1.a1'], 'contains': ['240.a1.a1', '240.e1.a1', '240.j1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4508, -1, 5398, -1, 4874, -1, 4861, -1], 'generators': [2, 516], 'label': '960.10966.120.d1.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.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595444
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '40.d1.a1', '60.b1.a1', '60.d1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.f1.a1', '240.k1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2677, -1, 7243, -1, 3665, -1, 3682, -1], 'generators': [5, 2], 'label': '960.10966.120.e1.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.e1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595445
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '60.a1.a1', '60.c1.a1', '60.e1.a1', '60.f1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1'], 'contains': ['240.a1.a1', '240.g1.a1', '240.h1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6121, -1, 3649, -1, 6639, -1, 6594, -1], 'generators': [2, 504], 'label': '960.10966.120.f1.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.f1.a1', 'projective_image': '480.1193', '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': '4.2'}
  • id: 112595446
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '40.e1.a1', '60.b1.a1', '60.j1.a1', '60.k1.a1'], 'contains': ['240.b1.a1', '240.c1.a1', '240.f1.a1', '240.m1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1705, -1, 8190, -1, 3183, -1, 3080, -1], 'generators': [1, 12, 480], 'label': '960.10966.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595447
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '40.f1.a1', '60.b1.a1', '60.j1.a1', '60.l1.a1'], 'contains': ['240.b1.a1', '240.d1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2955, -1, 6417, -1, 3803, -1, 3748, -1], 'generators': [3, 12], 'label': '960.10966.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595448
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.i1.a1', '12.k1.a1', '12.bh1.a1', '12.bj1.a1', '12.bk1.a1', '12.bm1.a1', '30.g1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8307, -1, 1148, -1, 5406, -1, 6000, -1], 'generators': [5, 192, 504, 720, 2, 480], 'label': '960.10966.6.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': '480.1193', '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': '160.217'}
  • id: 112595449
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '60.c1.a1', '60.j1.a1', '60.m1.a1'], 'contains': ['240.b1.a1', '240.e1.a1', '240.g1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4876, -1, 5220, -1, 4805, -1, 4795, -1], 'generators': [506, 12], 'label': '960.10966.120.i1.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.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595450
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '60.c1.a1', '60.k1.a1', '60.l1.a1', '60.m1.a1', '60.n1.a1', '60.o1.a1', '60.p1.a1'], 'contains': ['240.b1.a1', '240.h1.a1', '240.j1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5681, -1, 4390, -1, 6900, -1, 7364, -1], 'generators': [12, 504], 'label': '960.10966.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595451
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '60.e1.a1', '60.j1.a1', '60.q1.a1'], 'contains': ['240.c1.a1', '240.d1.a1', '240.g1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3779, -1, 5963, -1, 4218, -1, 4024, -1], 'generators': [1, 266], 'label': '960.10966.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595452
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '60.d1.a1', '60.j1.a1', '60.r1.a1'], 'contains': ['240.c1.a1', '240.e1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3835, -1, 5906, -1, 4080, -1, 4165, -1], 'generators': [1, 278], 'label': '960.10966.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595453
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '60.d1.a1', '60.k1.a1', '60.q1.a1'], 'contains': ['240.c1.a1', '240.f1.a1', '240.j1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3097, -1, 6196, -1, 4149, -1, 4231, -1], 'generators': [1, 276], 'label': '960.10966.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595454
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '40.g1.a1', '60.b1.a1', '60.q1.a1', '60.r1.a1'], 'contains': ['240.c1.a1', '240.i1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3463, -1, 6687, -1, 3902, -1, 3844, -1], 'generators': [1, 14], 'label': '960.10966.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595455
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '60.e1.a1', '60.k1.a1', '60.r1.a1', '60.s1.a1', '60.t1.a1', '60.u1.a1', '60.v1.a1'], 'contains': ['240.c1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5055, -1, 4637, -1, 6999, -1, 6946, -1], 'generators': [1, 264], 'label': '960.10966.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595456
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '60.d1.a1', '60.j1.a1', '60.w1.a1'], 'contains': ['240.d1.a1', '240.e1.a1', '240.f1.a1', '240.n1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3029, -1, 6138, -1, 4007, -1, 4094, -1], 'generators': [5, 254, 480], 'label': '960.10966.120.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.p1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595457
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '40.h1.a1', '60.b1.a1', '60.q1.a1', '60.w1.a1'], 'contains': ['240.d1.a1', '240.f1.a1', '240.i1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3288, -1, 6591, -1, 3734, -1, 3616, -1], 'generators': [5, 14], 'label': '960.10966.120.q1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.q1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595458
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '60.d1.a1', '60.l1.a1', '60.q1.a1'], 'contains': ['240.d1.a1', '240.j1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4201, -1, 5760, -1, 4447, -1, 4452, -1], 'generators': [3, 276], 'label': '960.10966.120.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.r1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595459
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.a1', '12.o1.a1', '12.q1.a1', '12.t1.a1', '12.u1.a1', '12.bf1.a1', '12.bh1.a1', '30.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7166, -1, 1241, -1, 6554, -1, 6528, -1], 'generators': [1, 192, 12, 264, 242, 480], 'label': '960.10966.6.h1.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.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595460
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '60.e1.a1', '60.l1.a1', '60.w1.a1', '60.x1.a1', '60.y1.a1', '60.z1.a1', '60.ba1.a1'], 'contains': ['240.d1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5523, -1, 3900, -1, 6540, -1, 7078, -1], 'generators': [3, 264], 'label': '960.10966.120.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.s1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595461
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.t1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '60.f1.a1', '60.m1.a1', '60.bb1.a1'], 'contains': ['240.e1.a1', '240.g1.a1', '240.j1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6228, -1, 4286, -1, 7098, -1, 7489, -1], 'generators': [242, 516], 'label': '960.10966.120.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.t1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595462
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.u1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '60.c1.a1', '60.r1.a1', '60.w1.a1', '60.bb1.a1', '60.bc1.a1', '60.bd1.a1', '60.bg1.a1'], 'contains': ['240.e1.a1', '240.h1.a1', '240.i1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6815, -1, 3303, -1, 6769, -1, 7239, -1], 'generators': [14, 504], 'label': '960.10966.120.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.u1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595463
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.v1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '120.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '60.f1.a1', '60.m1.a1', '60.s1.a1', '60.x1.a1', '60.be1.a1', '60.bf1.a1', '60.bg1.a1'], 'contains': ['240.e1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7964, -1, 2849, -1, 8041, -1, 8000, -1], 'generators': [254, 504], 'label': '960.10966.120.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.v1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595464
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.w1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '120.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '60.g1.a1', '60.j1.a1', '60.q1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4093, -1, 5643, -1, 4317, -1, 4327, -1], 'generators': [5, 242], 'label': '960.10966.120.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.w1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595465
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.x1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '120.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '60.g1.a1', '60.k1.a1', '60.w1.a1', '60.be1.a1', '60.bh1.a1', '60.bi1.a1', '60.bj1.a1'], 'contains': ['240.f1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5334, -1, 4914, -1, 6402, -1, 7012, -1], 'generators': [5, 240], 'label': '960.10966.120.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.x1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595466
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.y1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '60.c1.a1', '60.q1.a1', '60.bb1.a1'], 'contains': ['240.g1.a1', '240.i1.a1', '240.j1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4668, -1, 5342, -1, 4943, -1, 4928, -1], 'generators': [506, 516], 'label': '960.10966.120.y1.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.y1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595467
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '120.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '60.a1.a1', '60.m1.a1', '60.t1.a1', '60.y1.a1', '60.bb1.a1', '60.bh1.a1', '60.bk1.a1'], 'contains': ['240.g1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7084, -1, 2021, -1, 8139, -1, 8094, -1], 'generators': [242, 504], 'label': '960.10966.120.z1.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.z1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595468
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.ba1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '120.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '60.f1.a1', '60.p1.a1', '60.u1.a1', '60.z1.a1', '60.bb1.a1', '60.bi1.a1', '60.bl1.a1'], 'contains': ['240.h1.a1', '240.j1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6563, -1, 3385, -1, 8223, -1, 8175, -1], 'generators': [252, 504], 'label': '960.10966.120.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.ba1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595469
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '120.bb1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 480, 'centralizer': '120.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '60.g1.a1', '60.l1.a1', '60.r1.a1', '60.bf1.a1', '60.bk1.a1', '60.bl1.a1', '60.bm1.a1'], 'contains': ['240.h1.a1', '240.k1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5891, -1, 3775, -1, 7198, -1, 7144, -1], 'generators': [7, 240], 'label': '960.10966.120.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.bb1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 112595470
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.m1.a1', '12.p1.a1', '12.v1.a1', '12.w1.a1', '12.bi1.a1', '12.bj1.a1', '30.i1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8097, -1, 2165, -1, 6030, -1, 5842, -1], 'generators': [1, 192, 240, 264, 12, 480], 'label': '960.10966.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595471
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '120.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '60.h1.a1', '60.n1.a1', '60.v1.a1', '60.y1.a1', '60.bc1.a1', '60.bf1.a1', '60.bi1.a1'], 'contains': ['240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8889, -1, 1148, -1, 8694, -1, 8537, -1], 'generators': [241], 'label': '960.10966.120.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.bc1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595472
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '120.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '60.h1.a1', '60.o1.a1', '60.t1.a1', '60.ba1.a1', '60.bd1.a1', '60.be1.a1', '60.bl1.a1'], 'contains': ['240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8620, -1, 916, -1, 9246, -1, 8447, -1], 'generators': [243], 'label': '960.10966.120.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.bd1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595473
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.be1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '60.i1.a1', '60.o1.a1', '60.s1.a1', '60.z1.a1', '60.bc1.a1', '60.bh1.a1', '60.bm1.a1'], 'contains': ['240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8203, -1, 1438, -1, 8425, -1, 9057, -1], 'generators': [511], 'label': '960.10966.120.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.be1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595474
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '120.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 960, 'centralizer': '60.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '60.i1.a1', '60.n1.a1', '60.u1.a1', '60.x1.a1', '60.bd1.a1', '60.bj1.a1', '60.bk1.a1'], 'contains': ['240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8442, -1, 1555, -1, 9056, -1, 8970, -1], 'generators': [509], 'label': '960.10966.120.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.bf1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595475
    {'ambient': '960.10966', 'aut_centralizer_order': 480, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '40.a1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1', '80.d1.a1', '80.e1.a1', '80.f1.a1', '80.g1.a1'], 'contains': ['320.a1.a1', '480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1271, -1, 7941, -1, 1949, -1, 1945, -1], 'generators': [480, 8], 'label': '960.10966.160.a1.a1', 'mobius_quo': None, 'mobius_sub': -40, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '160.a1.a1', 'projective_image': '480.1193', '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: 112595476
    {'ambient': '960.10966', 'aut_centralizer_order': 240, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '80.a1.a1', '80.h1.a1', '80.h1.a2'], 'contains': ['320.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [267, -1, 9009, -1, 1417, -1, 701, -1], 'generators': [2, 8], 'label': '960.10966.160.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '160.b1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595477
    {'ambient': '960.10966', 'aut_centralizer_order': 48, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '80.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '80.b1.a1', '80.i1.a1', '80.i1.a2'], 'contains': ['320.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [59, -1, 9937, -1, 1126, -1, 1391, -1], 'generators': [12, 8], 'label': '960.10966.160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.e1.a1', 'old_label': '160.c1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595478
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '80.c1.a1', '80.h1.a1', '80.i1.a1'], 'contains': ['320.a1.a1', '480.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [176, -1, 9465, -1, 1195, -1, 1082, -1], 'generators': [1, 8], 'label': '960.10966.160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '160.d1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595479
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a2', '80.c1.a1', '80.h1.a2', '80.i1.a2'], 'contains': ['320.a1.a1', '480.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [176, -1, 9557, -1, 1195, -1, 940, -1], 'generators': [481, 8], 'label': '960.10966.160.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '160.d1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595480
    {'ambient': '960.10966', 'aut_centralizer_order': 80, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '80.d1.a1', '80.h1.a1', '80.h1.a2'], 'contains': ['320.a1.a1', '480.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [860, -1, 8774, -1, 1486, -1, 785, -1], 'generators': [3, 8], 'label': '960.10966.160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '160.e1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595481
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.n1.a1', '12.o1.a1', '12.p1.a1', '12.y1.a1', '12.z1.a1', '12.bg1.a1', '12.bk1.a1', '30.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8448, -1, 2427, -1, 6815, -1, 6409, -1], 'generators': [241, 192, 12, 264, 242, 480], 'label': '960.10966.6.j1.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.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595482
    {'ambient': '960.10966', 'aut_centralizer_order': 16, 'aut_label': '160.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 640, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '80.e1.a1', '80.i1.a1', '80.i1.a2'], 'contains': ['320.a1.a1', '480.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [357, -1, 9714, -1, 1348, -1, 1457, -1], 'generators': [5, 8], 'label': '960.10966.160.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.e1.a1', 'old_label': '160.f1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595483
    {'ambient': '960.10966', 'aut_centralizer_order': 960, 'aut_label': '192.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 960, 'centralizer': '2.b1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1', '96.g1.a1'], 'contains': ['960.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [700, 3181, 9115, 7175, 2112, 2719, 1672, 2581], 'generators': [192], 'label': '960.10966.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '960.10966', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.189', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595501
    {'ambient': '960.10966', 'aut_centralizer_order': 1920, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '160.b1.a1', '240.a1.a1', '240.l1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [644, -1, 8875, -1, 2043, -1, 1236, -1], 'generators': [2], 'label': '960.10966.480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '480.b1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595484
    {'ambient': '960.10966', 'aut_centralizer_order': 1920, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.f1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2094, 4064, 7434, 6088, 3399, 3263, 3151, 3125], 'generators': [2, 480], 'label': '960.10966.240.a1.a1', 'mobius_quo': 0, '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': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.37', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595485
    {'ambient': '960.10966', 'aut_centralizer_order': 384, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '10.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.b1.a1', '120.b1.a1', '120.g1.a1', '120.h1.a1', '120.i1.a1', '120.j1.a1'], 'contains': ['480.a1.a1', '480.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1730, -1, 8139, -1, 3320, -1, 3390, -1], 'generators': [12, 480], 'label': '960.10966.240.b1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '480.1193', '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': '2.1'}
  • id: 112595486
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '80.c1.a1', '120.c1.a1', '120.g1.a1', '120.k1.a1', '120.l1.a1', '120.m1.a1', '120.n1.a1', '120.o1.a1'], 'contains': ['480.a1.a1', '480.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2030, -1, 7185, -1, 3477, -1, 3234, -1], 'generators': [1, 480], 'label': '960.10966.240.c1.a1', 'mobius_quo': None, 'mobius_sub': -20, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '240.c1.a1', 'projective_image': '480.1193', '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': '2.1'}
  • id: 112595487
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '80.d1.a1', '120.c1.a1', '120.h1.a1', '120.k1.a1', '120.p1.a1', '120.q1.a1', '120.r1.a1', '120.s1.a1'], 'contains': ['480.a1.a1', '480.e1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2882, -1, 6484, -1, 3712, -1, 3465, -1], 'generators': [3, 480], 'label': '960.10966.240.d1.a1', 'mobius_quo': None, 'mobius_sub': -20, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '480.1193', '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': '2.1'}
  • id: 112595488
    {'ambient': '960.10966', 'aut_centralizer_order': 128, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '30.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '120.d1.a1', '120.i1.a1', '120.l1.a1', '120.p1.a1', '120.t1.a1', '120.u1.a1', '120.v1.a1'], 'contains': ['480.a1.a1', '480.f1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5011, -1, 5236, -1, 4643, -1, 4640, -1], 'generators': [518, 480], 'label': '960.10966.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '240.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595489
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '80.e1.a1', '120.e1.a1', '120.g1.a1', '120.m1.a1', '120.p1.a1', '120.q1.a1', '120.w1.a1', '120.x1.a1'], 'contains': ['480.a1.a1', '480.g1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2554, -1, 7651, -1, 3634, -1, 3616, -1], 'generators': [5, 480], 'label': '960.10966.240.f1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595490
    {'ambient': '960.10966', 'aut_centralizer_order': 640, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '120.f1.a1', '120.i1.a1', '120.k1.a1', '120.t1.a1', '120.w1.a1', '120.y1.a1', '120.z1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4847, -1, 5382, -1, 4805, -1, 4795, -1], 'generators': [506], 'label': '960.10966.240.g1.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': '240.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595491
    {'ambient': '960.10966', 'aut_centralizer_order': 640, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '120.a1.a1', '120.f1.a1', '120.j1.a1', '120.o1.a1', '120.s1.a1', '120.u1.a1', '120.v1.a1', '120.x1.a1', '120.z1.a1', '120.ba1.a1', '120.bb1.a1', '120.bc1.a1', '120.bd1.a1', '120.be1.a1', '120.bf1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6849, -1, 3303, -1, 6999, -1, 7239, -1], 'generators': [504], 'label': '960.10966.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595492
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.n1.a1', '12.q1.a1', '12.ba1.a1', '12.bb1.a1', '12.bl1.a1', '12.bm1.a1', '30.k1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6602, -1, 2002, -1, 6198, -1, 6117, -1], 'generators': [3, 192, 240, 264, 12, 480], 'label': '960.10966.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595493
    {'ambient': '960.10966', 'aut_centralizer_order': 384, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '10.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.f1.a1', '120.b1.a1', '120.n1.a1', '120.q1.a1', '120.u1.a1', '120.y1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3446, -1, 7084, -1, 3855, -1, 3753, -1], 'generators': [14], 'label': '960.10966.240.i1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '240.i1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595494
    {'ambient': '960.10966', 'aut_centralizer_order': 128, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '30.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '120.d1.a1', '120.j1.a1', '120.m1.a1', '120.r1.a1', '120.t1.a1', '120.y1.a1', '120.ba1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4508, -1, 5673, -1, 4874, -1, 4861, -1], 'generators': [516], 'label': '960.10966.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '240.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595495
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '60.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '80.g1.a1', '120.e1.a1', '120.h1.a1', '120.l1.a1', '120.n1.a1', '120.r1.a1', '120.w1.a1', '120.bb1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3344, -1, 5986, -1, 3923, -1, 3896, -1], 'generators': [7], 'label': '960.10966.240.k1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595496
    {'ambient': '960.10966', 'aut_centralizer_order': 160, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '80.h1.a1', '80.h1.a2', '120.c1.a1'], 'contains': ['480.b1.a1', '480.d1.a1', '480.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [613, -1, 8699, -1, 2107, -1, 1011, -1], 'generators': [1, 2], 'label': '960.10966.240.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '240.l1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595497
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '240.m1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '80.i1.a1', '80.i1.a2', '120.g1.a1'], 'contains': ['480.c1.a1', '480.d1.a1', '480.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [488, -1, 9927, -1, 1792, -1, 1527, -1], 'generators': [1, 12], 'label': '960.10966.240.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1.a1', 'old_label': '240.m1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595498
    {'ambient': '960.10966', 'aut_centralizer_order': 32, 'aut_label': '240.n1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '120.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '120.p1.a1'], 'contains': ['480.e1.a1', '480.f1.a1', '480.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [2158, -1, 7010, -1, 3555, -1, 3541, -1], 'generators': [5, 254], 'label': '960.10966.240.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.p1.a1', 'old_label': '240.n1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595499
    {'ambient': '960.10966', 'aut_centralizer_order': 480, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1920, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1', '160.d1.a1', '160.d1.a2', '160.e1.a1', '160.f1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [277, -1, 9480, -1, 1382, -1, 1155, -1], 'generators': [8], 'label': '960.10966.320.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '320.a1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112595500
    {'ambient': '960.10966', 'aut_centralizer_order': 3840, 'aut_label': '480.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '240.d1.a1', '240.e1.a1', '240.f1.a1', '240.g1.a1', '240.h1.a1', '240.i1.a1', '240.j1.a1', '240.k1.a1'], 'contains': ['960.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2330, 3903, 7185, 6649, 3655, 3188, 3470, 3050], 'generators': [480], 'label': '960.10966.480.a1.a1', 'mobius_quo': -1, 'mobius_sub': 480, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['96.a1.a1', '120.a1.a1', '240.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '480.1193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.1193', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595503
    {'ambient': '960.10966', 'aut_centralizer_order': 10, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20048', 'aut_weyl_index': 10, 'centralizer': '48.a1.a1', 'complements': ['480.c1.a1', '480.f1.a1', '480.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.e1.a1', '8.c1.a1', '10.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5335, 9559, 4700, 778, 2295, 8719, 2007, 8563], 'generators': [1, 240, 192, 8, 2, 480, 264], 'label': '960.10966.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.c1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595504
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.s1.a1', '12.u1.a1', '12.v1.a1', '12.bc1.a1', '12.be1.a1', '12.bk1.a1', '12.bl1.a1', '30.l1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6748, -1, 3066, -1, 7503, -1, 6672, -1], 'generators': [1, 192, 252, 264, 242, 480], 'label': '960.10966.6.l1.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.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595505
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '160.d1.a1', '160.d1.a2', '240.c1.a1', '240.l1.a1', '240.m1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [573, -1, 9327, -1, 1923, -1, 1317, -1], 'generators': [1], 'label': '960.10966.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '480.d1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595506
    {'ambient': '960.10966', 'aut_centralizer_order': 320, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '160.e1.a1', '240.d1.a1', '240.l1.a1', '240.n1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [919, -1, 8639, -1, 2253, -1, 1605, -1], 'generators': [3], 'label': '960.10966.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '480.e1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595507
    {'ambient': '960.10966', 'aut_centralizer_order': 128, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '30.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '240.e1.a1', '240.n1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2388, -1, 6952, -1, 3765, -1, 3613, -1], 'generators': [518], 'label': '960.10966.480.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.n1.a1', 'old_label': '480.f1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595508
    {'ambient': '960.10966', 'aut_centralizer_order': 64, 'aut_label': '480.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3840, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '160.f1.a1', '240.f1.a1', '240.m1.a1', '240.n1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [834, -1, 9413, -1, 2181, -1, 1741, -1], 'generators': [5], 'label': '960.10966.480.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.j1.a1', 'old_label': '480.g1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595509
    {'ambient': '960.10966', 'aut_centralizer_order': None, 'aut_label': '960.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': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1', '480.d1.a1', '480.e1.a1', '480.f1.a1', '480.g1.a1'], 'contains': [], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [687, 3611, 9044, 6884, 2112, 2944, 1605, 2806], 'generators': [], 'label': '960.10966.960.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '960.a1.a1', 'normal_contained_in': ['192.a1.a1', '480.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112595510
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.s1.a1', '12.t1.a1', '12.w1.a1', '12.bd1.a1', '12.bg1.a1', '12.bm1.a1', '30.m1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7603, -1, 1540, -1, 5532, -1, 5676, -1], 'generators': [1, 192, 240, 264, 14, 480], 'label': '960.10966.6.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595511
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.x1.a1', '12.z1.a1', '12.ba1.a1', '12.bc1.a1', '12.bd1.a1', '12.bh1.a1', '12.bi1.a1', '30.n1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7345, -1, 2926, -1, 5705, -1, 6833, -1], 'generators': [241, 192, 252, 264, 242, 480], 'label': '960.10966.6.n1.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.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595512
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.x1.a1', '12.y1.a1', '12.bb1.a1', '12.be1.a1', '12.bf1.a1', '12.bj1.a1', '30.o1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7964, -1, 1702, -1, 5868, -1, 5557, -1], 'generators': [5, 192, 504, 720, 14, 480], 'label': '960.10966.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595513
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['24.b1.a1', '32.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5095, 4909, 5027, 5633, 1888, 4400, 2520, 4450], 'generators': [8, 504, 240, 192, 480], 'label': '960.10966.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.c1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['24.b1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '480.1193', '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': '48.48'}
  • id: 112595514
    {'ambient': '960.10966', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.f1.a1', '24.a1.a1', '40.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1303, -1, 8185, -1, 822, -1, 1419, -1], 'generators': [2, 8, 480, 12, 192], 'label': '960.10966.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.b1.a1', 'projective_image': '480.1193', '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': '40.13'}
  • id: 112595515
    {'ambient': '960.10966', 'aut_centralizer_order': 10, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.h1.a1', '16.h1.a2', '24.c1.a1', '40.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1069, -1, 8707, -1, 593, -1, 719, -1], 'generators': [1, 480, 192, 2, 8], 'label': '960.10966.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.c1.a1', 'projective_image': '480.1193', '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': '12.4'}
  • id: 112595516
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 8, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.g1.a1', '24.e1.a1', '40.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1512, -1, 7979, -1, 995, -1, 1710, -1], 'generators': [5, 480, 8, 2, 192], 'label': '960.10966.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595517
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 8, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1', '16.i1.a1', '16.i1.a2', '24.g1.a1', '40.e1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [673, -1, 9367, -1, 341, -1, 961, -1], 'generators': [1, 480, 8, 12, 192], 'label': '960.10966.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595518
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 8, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.g1.a1', '24.h1.a1', '40.f1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1783, -1, 7603, -1, 1260, -1, 1819, -1], 'generators': [3, 480, 8, 12, 192], 'label': '960.10966.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595519
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.c1.a1', '480.f1.a1', '480.d1.a1', '480.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.g1.a1', '8.d1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4770, 6474, 5090, 2605, 1608, 4887, 2570, 4644], 'generators': [5, 240, 8, 192, 2, 480, 744], 'label': '960.10966.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '480.1193', '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': '480.1193'}
  • id: 112595520
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 8, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.h1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.g1.a1', '24.n1.a1', '40.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2188, -1, 7419, -1, 1506, -1, 2055, -1], 'generators': [1, 480, 8, 14, 192], 'label': '960.10966.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595521
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 8, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.h1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.q1.a1', '40.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1900, -1, 8373, -1, 1109, -1, 1253, -1], 'generators': [5, 480, 8, 14, 192], 'label': '960.10966.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.h1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595522
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '48.a1.a1', 'complements': ['96.c1.a1', '96.f1.a1', '96.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.e1.a1', '40.c1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 8485, 4773, 2896, 3051, 9400, 2818, 9400], 'generators': [1, 480, 240, 2, 8, 264], 'label': '960.10966.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['20.a1.a1', '20.c1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '480.1193', '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: 112595523
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.e1.a1', '20.f1.a1', '30.c1.a1', '40.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4662, -1, 5460, -1, 2476, -1, 3504, -1], 'generators': [2, 480, 240, 12, 8, 744], 'label': '960.10966.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '480.1193', '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': '96.226'}
  • id: 112595524
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.g1.a1', '20.h1.a1', '30.g1.a1', '40.d1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4746, -1, 5019, -1, 2577, -1, 3407, -1], 'generators': [5, 480, 240, 2, 8, 744], 'label': '960.10966.10.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': '480.1193', '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': '96.226'}
  • id: 112595525
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.e1.a1', '20.g1.a1', '30.i1.a1', '40.e1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5357, -1, 5634, -1, 2735, -1, 3255, -1], 'generators': [1, 480, 240, 12, 8, 264], 'label': '960.10966.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595526
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.e1.a1', '20.h1.a1', '30.k1.a1', '40.f1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5033, -1, 4928, -1, 2893, -1, 3601, -1], 'generators': [3, 480, 240, 12, 8, 264], 'label': '960.10966.10.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 112595527
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '240.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.f1.a1', '20.h1.a1', '30.m1.a1', '40.g1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4874, -1, 5173, -1, 3214, -1, 3717, -1], 'generators': [1, 480, 240, 14, 8, 264], 'label': '960.10966.10.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595528
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '10.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.226', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.f1.a1', '20.g1.a1', '30.o1.a1', '40.h1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4539, -1, 5310, -1, 3348, -1, 2982, -1], 'generators': [5, 480, 240, 14, 8, 744], 'label': '960.10966.10.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.g1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 112595529
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 20, 'centralizer': '48.a1.a1', 'complements': ['80.i1.a1', '80.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '24.z1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6890, 5024, 2844, 6102, 4538, 3231, 4771, 3194], 'generators': [2, 240, 192, 504, 480], 'label': '960.10966.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '480.1193', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 112595530
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.b1.a1', '480.f1.a1', '480.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '6.i1.a1', '8.e1.a1', '10.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5524, 2675, 5683, 6969, 1841, 6413, 2346, 2213], 'generators': [1, 240, 8, 192, 12, 480, 264], 'label': '960.10966.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595531
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['80.h1.a1', '80.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.ba1.a1', '60.p1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6291, 2859, 3387, 8711, 5284, 1413, 5530, 2200], 'generators': [12, 240, 480, 504, 192], 'label': '960.10966.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '480.1193', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595532
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 4, 'centralizer': '480.a1.a1', 'complements': ['80.i1.a1', '80.i1.a2', '80.h1.a1', '80.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.m1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.u1.a1', '24.v1.a1', '60.bg1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6632, 1792, 3494, 7452, 4684, 2281, 4911, 1194], 'generators': [14, 240, 480, 504, 192], 'label': '960.10966.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '480.1193', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595533
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.e1.a1', '24.g1.a1', '24.h1.a1', '24.n1.a1', '24.q1.a1', '60.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1913, -1, 7637, -1, 3067, -1, 2348, -1], 'generators': [1, 12, 480, 2, 192], 'label': '960.10966.12.d1.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.d1.a1', 'projective_image': '480.1193', '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': '40.13'}
  • id: 112595534
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.f1.a1', '24.i1.a1', '24.j1.a1', '24.u1.a1', '24.y1.a1', '60.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3740, -1, 5830, -1, 3583, -1, 3854, -1], 'generators': [2, 504, 480, 12, 192], 'label': '960.10966.12.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': '480.1193', '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: 112595535
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1', '24.l1.a1', '24.m1.a1', '24.p1.a1', '24.r1.a1', '60.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2352, -1, 7050, -1, 3358, -1, 3637, -1], 'generators': [1, 276, 480, 2, 192], 'label': '960.10966.12.f1.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.f1.a1', 'projective_image': '480.1193', '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': '40.13'}
  • id: 112595536
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.k1.a1', '24.o1.a1', '24.s1.a1', '60.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4229, -1, 4589, -1, 3981, -1, 3984, -1], 'generators': [1, 264, 192, 2, 480], 'label': '960.10966.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '480.1193', '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': '16.11'}
  • id: 112595537
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.d1.a1', '24.f1.a1', '24.t1.a1', '24.v1.a1', '24.ba1.a1', '60.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5963, -1, 4358, -1, 4942, -1, 5886, -1], 'generators': [2, 504, 480, 252, 192], 'label': '960.10966.12.h1.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.h1.a1', 'projective_image': '480.1193', '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': '80.39'}
  • id: 112595538
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.w1.a1', '24.x1.a1', '24.bb1.a1', '60.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4347, -1, 6091, -1, 4117, -1, 4241, -1], 'generators': [5, 240, 480, 2, 192], 'label': '960.10966.12.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': '480.1193', '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': '80.39'}
  • id: 112595539
    {'ambient': '960.10966', 'aut_centralizer_order': 40, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.45', 'aut_weyl_index': 120, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.bc1.a1', '24.bd1.a1', '60.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9237, -1, 342, -1, 7854, -1, 6715, -1], 'generators': [241, 192, 264, 2, 480], 'label': '960.10966.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112595540
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.f1.a1', '24.be1.a1', '24.bf1.a1', '60.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8536, -1, 740, -1, 6893, -1, 8198, -1], 'generators': [509, 720, 480, 2, 192], 'label': '960.10966.12.k1.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.k1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595541
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.b1.a1', '480.f1.a1', '480.d1.a1', '480.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '6.k1.a1', '8.f1.a1', '10.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5143, 4448, 4889, 5328, 2062, 3238, 2934, 7038], 'generators': [3, 240, 8, 192, 12, 480, 264], 'label': '960.10966.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595542
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '24.l1.a1', '24.p1.a1', '24.w1.a1', '60.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2899, -1, 6672, -1, 3212, -1, 3497, -1], 'generators': [1, 12, 480, 266, 192], 'label': '960.10966.12.l1.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.l1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '80.51'}
  • id: 112595543
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.g1.a1', '24.j1.a1', '24.m1.a1', '24.o1.a1', '24.x1.a1', '60.k1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4003, -1, 6275, -1, 3836, -1, 4123, -1], 'generators': [1, 264, 480, 12, 192], 'label': '960.10966.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595544
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.r1.a1', '24.s1.a1', '24.bb1.a1', '60.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5598, -1, 4277, -1, 4218, -1, 4549, -1], 'generators': [3, 264, 480, 12, 192], 'label': '960.10966.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595545
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.i1.a1', '24.j1.a1', '24.t1.a1', '24.v1.a1', '24.z1.a1', '60.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5861, -1, 3852, -1, 4817, -1, 5767, -1], 'generators': [242, 504, 480, 12, 192], 'label': '960.10966.12.o1.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.o1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595546
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.j1.a1', '24.bc1.a1', '24.bf1.a1', '60.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9847, -1, 943, -1, 7331, -1, 7683, -1], 'generators': [241, 264, 480, 12, 192], 'label': '960.10966.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595547
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.j1.a1', '24.bd1.a1', '24.be1.a1', '60.o1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8174, -1, 188, -1, 7095, -1, 8089, -1], 'generators': [243, 264, 480, 12, 192], 'label': '960.10966.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595548
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.k1.a1', '24.m1.a1', '24.n1.a1', '24.q1.a1', '24.r1.a1', '24.w1.a1', '24.y1.a1', '60.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3078, -1, 6847, -1, 3482, -1, 3757, -1], 'generators': [1, 276, 480, 266, 192], 'label': '960.10966.12.r1.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.r1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '80.51'}
  • id: 112595549
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.l1.a1', '24.n1.a1', '24.o1.a1', '24.u1.a1', '24.bb1.a1', '60.r1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3824, -1, 5488, -1, 4307, -1, 4464, -1], 'generators': [1, 264, 480, 14, 192], 'label': '960.10966.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595550
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.m1.a1'], 'contains': ['24.o1.a1', '24.v1.a1', '24.be1.a1', '60.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7080, -1, 2526, -1, 6019, -1, 7002, -1], 'generators': [1, 264, 480, 254, 192], 'label': '960.10966.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595551
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '6.l1.a1'], 'contains': ['24.o1.a1', '24.z1.a1', '24.bd1.a1', '60.t1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7569, -1, 1080, -1, 7503, -1, 6336, -1], 'generators': [1, 192, 264, 242, 480], 'label': '960.10966.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595552
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.c1.a1', '480.b1.a1', '480.g1.a1', '480.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1', '6.m1.a1', '8.g1.a1', '10.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4983, 1409, 5245, 4012, 2466, 2081, 3104, 5881], 'generators': [1, 240, 8, 192, 14, 480, 264], 'label': '960.10966.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595553
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '6.l1.a1'], 'contains': ['24.o1.a1', '24.ba1.a1', '24.bf1.a1', '60.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6756, -1, 3267, -1, 7692, -1, 7430, -1], 'generators': [1, 264, 480, 252, 192], 'label': '960.10966.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595554
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1', '6.i1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.o1.a1', '24.bc1.a1', '60.v1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8979, -1, 1467, -1, 5569, -1, 5280, -1], 'generators': [1, 192, 264, 240, 480], 'label': '960.10966.12.w1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595555
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.p1.a1', '24.q1.a1', '24.s1.a1', '24.u1.a1', '24.x1.a1', '60.w1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4110, -1, 5990, -1, 3705, -1, 4358, -1], 'generators': [5, 240, 480, 14, 192], 'label': '960.10966.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595556
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.s1.a1', '24.v1.a1', '24.bf1.a1', '60.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7917, -1, 2718, -1, 6706, -1, 6917, -1], 'generators': [509, 720, 480, 518, 192], 'label': '960.10966.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595557
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.s1.a1', '24.z1.a1', '24.bc1.a1', '60.y1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8669, -1, 2244, -1, 6468, -1, 6538, -1], 'generators': [241, 192, 264, 242, 480], 'label': '960.10966.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595558
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.k1.a1', '6.n1.a1'], 'contains': ['24.s1.a1', '24.ba1.a1', '24.be1.a1', '60.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6414, -1, 3132, -1, 6147, -1, 7827, -1], 'generators': [3, 744, 480, 252, 192], 'label': '960.10966.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595559
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.196', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.e1.a1', '6.k1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.s1.a1', '24.bd1.a1', '60.ba1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8040, -1, 610, -1, 5869, -1, 5077, -1], 'generators': [3, 192, 264, 240, 480], 'label': '960.10966.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 112595560
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.t1.a1', '24.u1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '60.bb1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5508, -1, 3969, -1, 5064, -1, 6004, -1], 'generators': [242, 504, 480, 252, 192], 'label': '960.10966.12.bc1.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.bc1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595561
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.u1.a1', '24.bc1.a1', '24.be1.a1', '60.bc1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9120, -1, 838, -1, 6297, -1, 7971, -1], 'generators': [241, 264, 480, 14, 192], 'label': '960.10966.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595562
    {'ambient': '960.10966', 'aut_centralizer_order': 8, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 24, 'centralizer': '120.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.l1.a1', '6.o1.a1'], 'contains': ['24.u1.a1', '24.bd1.a1', '24.bf1.a1', '60.bd1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8846, -1, 480, -1, 8103, -1, 7565, -1], 'generators': [509, 720, 480, 14, 192], 'label': '960.10966.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595563
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 2, 'centralizer': '480.a1.a1', 'complements': ['480.c1.a1', '480.b1.a1', '480.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.o1.a1', '8.h1.a1', '10.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4505, 8094, 5346, 8234, 2592, 7525, 2182, 3325], 'generators': [5, 240, 8, 192, 14, 480, 744], 'label': '960.10966.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1193'}
  • id: 112595564
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.o1.a1'], 'contains': ['24.v1.a1', '24.x1.a1', '24.bd1.a1', '60.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7151, -1, 1700, -1, 6793, -1, 6108, -1], 'generators': [5, 240, 480, 518, 192], 'label': '960.10966.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bf1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595565
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.m1.a1'], 'contains': ['24.v1.a1', '24.bb1.a1', '24.bc1.a1', '60.bf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7845, -1, 2364, -1, 6994, -1, 6191, -1], 'generators': [241, 264, 480, 254, 192], 'label': '960.10966.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595566
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.x1.a1', '24.z1.a1', '24.be1.a1', '60.bh1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7325, -1, 1200, -1, 5719, -1, 7196, -1], 'generators': [5, 240, 480, 506, 192], 'label': '960.10966.12.bh1.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.bh1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595567
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.n1.a1'], 'contains': ['24.x1.a1', '24.ba1.a1', '24.bc1.a1', '60.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7223, -1, 2943, -1, 6618, -1, 6832, -1], 'generators': [241, 264, 480, 252, 192], 'label': '960.10966.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595568
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.g1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.x1.a1', '24.bf1.a1', '60.bj1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8415, -1, 1609, -1, 5174, -1, 5424, -1], 'generators': [5, 720, 480, 504, 192], 'label': '960.10966.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bj1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595569
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.j1.a1', '6.l1.a1'], 'contains': ['24.z1.a1', '24.bb1.a1', '24.bf1.a1', '60.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8328, -1, 2445, -1, 7210, -1, 7099, -1], 'generators': [509, 720, 480, 506, 192], 'label': '960.10966.12.bk1.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.bk1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595570
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.k1.a1', '6.l1.a1'], 'contains': ['24.ba1.a1', '24.bb1.a1', '24.bd1.a1', '60.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6531, -1, 2637, -1, 7989, -1, 7293, -1], 'generators': [243, 264, 480, 252, 192], 'label': '960.10966.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bl1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '80.39'}
  • id: 112595571
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.g1.a1', '6.k1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.bb1.a1', '24.be1.a1', '60.bm1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7732, -1, 1281, -1, 5406, -1, 5648, -1], 'generators': [7, 720, 480, 504, 192], 'label': '960.10966.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bm1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '160.217'}
  • id: 112595572
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.261', 'aut_weyl_index': 60, 'centralizer': '480.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', '30.h1.a1', '30.i1.a1', '30.j1.a1', '30.k1.a1', '30.l1.a1', '30.m1.a1', '30.n1.a1', '30.o1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8297, -1, 1875, -1, 8862, -1, 9011, -1], 'generators': [1, 2, 12, 240], 'label': '960.10966.15.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': '480.1193', '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': '32.46'}
  • id: 112595573
    {'ambient': '960.10966', 'aut_centralizer_order': 60, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 240, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '48.a1.a1', '80.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [850, -1, 8417, -1, 641, -1, 906, -1], 'generators': [2, 8, 192, 480], 'label': '960.10966.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.a1.a1', 'projective_image': '480.1193', '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: 112595574
    {'ambient': '960.10966', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1280.1116277', 'aut_weyl_index': 3, 'centralizer': '480.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', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1', '6.o1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7603, -1, 1933, -1, 6198, -1, 6117, -1], 'generators': [1, 480, 12, 240, 2, 192, 264], 'label': '960.10966.3.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': '480.1193', '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': '160.217'}
  • id: 112595575
    {'ambient': '960.10966', 'aut_centralizer_order': 12, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.b1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '48.b1.a1', '80.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [539, -1, 9367, -1, 342, -1, 1419, -1], 'generators': [12, 8, 192, 480], 'label': '960.10966.16.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.b1.a1', 'projective_image': '480.1193', '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': '40.13'}
  • id: 112595576
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.c1.a1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.a2', '48.d1.a1', '80.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1105, -1, 9252, -1, 486, -1, 757, -1], 'generators': [1, 192, 8, 480], 'label': '960.10966.16.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.c1.a1', 'projective_image': '480.1193', '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': '12.4'}
  • id: 112595577
    {'ambient': '960.10966', 'aut_centralizer_order': 20, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 80, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.c1.a1', '8.f1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.e1.a1', '80.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [978, -1, 8681, -1, 882, -1, 1056, -1], 'generators': [3, 192, 8, 480], 'label': '960.10966.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.d1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112595578
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 16, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.d1.a1', '8.e1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '48.g1.a1', '80.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [728, -1, 8585, -1, 762, -1, 1315, -1], 'generators': [5, 8, 192, 480], 'label': '960.10966.16.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.e1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595579
    {'ambient': '960.10966', 'aut_centralizer_order': 12, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 48, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.b1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '80.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2610, -1, 7972, -1, 1338, -1, 1837, -1], 'generators': [14, 480, 192, 8], 'label': '960.10966.16.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.f1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 112595580
    {'ambient': '960.10966', 'aut_centralizer_order': 4, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 16, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.d1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '48.k1.a1', '80.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2021, -1, 7402, -1, 1475, -1, 2262, -1], 'generators': [7, 8, 192, 480], 'label': '960.10966.16.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.g1.a1', 'projective_image': '480.1193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 112595581
    {'ambient': '960.10966', 'aut_centralizer_order': 10, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.5', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1', '48.l1.a1', '80.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [320, -1, 8976, -1, 199, -1, 215, -1], 'generators': [1, 192, 8, 2], 'label': '960.10966.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.h1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595582
    {'ambient': '960.10966', 'aut_centralizer_order': 10, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.5', 'aut_weyl_index': 160, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.a1', '32.d1.a2', '32.e1.a1', '48.l1.a1', '80.h1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [320, -1, 9099, -1, 199, -1, 66, -1], 'generators': [481, 192, 8, 2], 'label': '960.10966.16.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.h1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112595583
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '120.36', 'aut_weyl_index': 32, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.f1.a1', '48.m1.a1', '80.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [172, -1, 9740, -1, 56, -1, 477, -1], 'generators': [1, 8, 192, 12], 'label': '960.10966.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.i1.a1', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 112595584
    {'ambient': '960.10966', 'aut_centralizer_order': 2, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '120.36', 'aut_weyl_index': 32, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.c1.a1', '32.d1.a2', '32.f1.a1', '48.m1.a1', '80.i1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [172, -1, 9915, -1, 56, -1, 352, -1], 'generators': [481, 8, 192, 12], 'label': '960.10966.16.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.i1.a2', 'projective_image': '960.10966', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a2', 'subgroup_fusion': None, 'weyl_group': '60.8'}