Abstract group data - 3960.o

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 2], 'aut_gens': [[6785983586, 1089851041], [45274781045, 19160161225], [59730175585, 59422694642]], 'aut_group': '7920.q', 'aut_hash': 1157788818429169362, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7920, 'aut_permdeg': 58, 'aut_perms': [587897353636398588644797072549007850204173044572507477404105747126651443728771, 23427148710332319059999225189100172835085593432025207827219142312268916422626], 'aut_phi_ratio': 8.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 55, 1, 1], [2, 165, 1, 1], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [5, 132, 1, 2], [6, 110, 1, 2], [6, 220, 1, 1], [6, 330, 1, 2], [10, 396, 1, 2], [11, 60, 2, 1], [15, 264, 1, 2], [22, 180, 2, 1], [33, 120, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times \\PGL(2,11)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '7920.q', 'autcentquo_hash': 1157788818429169362, 'autcentquo_nilpotent': False, 'autcentquo_order': 7920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times \\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 55, 1], [2, 165, 1], [3, 2, 1], [3, 110, 1], [3, 220, 1], [5, 132, 2], [6, 110, 2], [6, 220, 1], [6, 330, 2], [10, 396, 2], [11, 60, 2], [15, 264, 2], [22, 180, 2], [33, 120, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '3960.o', 'commutator_count': 1, 'commutator_label': '1980.57', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '660.13'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 1], ['660.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 55, 1, 1], [2, 165, 1, 1], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [5, 132, 2, 1], [6, 110, 1, 2], [6, 220, 1, 1], [6, 330, 1, 2], [10, 396, 2, 1], [11, 60, 2, 1], [15, 264, 2, 1], [22, 180, 2, 1], [33, 120, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 762, 'exponent': 330, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 0, 2], [20, 1, 2], [22, 1, 1], [24, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3960.o', 'hash': 6655759197249528573, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [10, 6], 'inner_gens': [[6785983586, 37864835429], [19452708005, 1089851041]], 'inner_hash': 6655759197249528573, 'inner_nilpotent': False, 'inner_order': 3960, 'inner_split': True, 'inner_tex': 'S_3\\times \\PSL(2,11)', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 2], [2, 1], [5, 4], [10, 6], [11, 2], [12, 4], [20, 2], [22, 1], [24, 2]], 'label': '3960.o', 'linC_count': 4, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 6, 'linQ_dim': 12, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S3*PSL(2,11)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 24, 'number_divisions': 18, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 75, 'number_subgroup_classes': 88, 'number_subgroups': 7504, 'old_label': None, 'order': 3960, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 223], [3, 332], [5, 264], [6, 1100], [10, 792], [11, 120], [15, 528], [22, 360], [33, 240]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [53460381024], 'outer_gens': [[58530145082, 56723690425]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [10, 6], [11, 2], [20, 3], [22, 1], [24, 2], [48, 1]], 'representations': {'Perm': {'d': 14, 'gens': [6785983586, 1089851041]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times \\PSL(2,11)', 'transitive_degree': 33, '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: 110096706
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 15, 'group_order': 3960, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 110096717
    {'aut_label': '2A', 'centralizer': '3.a1.a1', 'counter': 2, 'group_counter': 15, 'group_order': 3960, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 5, 'size': 3}
  • id: 110096723
    {'aut_label': '2B', 'centralizer': '55.b1.a1', 'counter': 3, 'group_counter': 15, 'group_order': 3960, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 50474124000, 'size': 55}
  • id: 110096724
    {'aut_label': '2C', 'centralizer': '165.b1.a1', 'counter': 4, 'group_counter': 15, 'group_order': 3960, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 21755830321, 'size': 165}
  • id: 110096725
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 15, 'group_order': 3960, 'label': '3A', 'order': 3, 'powers': [5, 1, 5, 5], 'representative': 3, 'size': 2}
  • id: 110096726
    {'aut_label': '3B', 'centralizer': '110.a1.a1', 'counter': 6, 'group_counter': 15, 'group_order': 3960, 'label': '3B', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 1440679104, 'size': 110}
  • id: 110096727
    {'aut_label': '3C', 'centralizer': '220.b1.a1', 'counter': 7, 'group_counter': 15, 'group_order': 3960, 'label': '3C', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 35776824508, 'size': 220}
  • id: 110096728
    {'aut_label': '5A1', 'centralizer': '132.a1.a1', 'counter': 8, 'group_counter': 15, 'group_order': 3960, 'label': '5A1', 'order': 5, 'powers': [9, 9, 1, 8], 'representative': 57533299464, 'size': 132}
  • id: 110096729
    {'aut_label': '5A2', 'centralizer': '132.a1.a1', 'counter': 9, 'group_counter': 15, 'group_order': 3960, 'label': '5A2', 'order': 5, 'powers': [8, 8, 1, 9], 'representative': 46118461800, 'size': 132}
  • id: 110096707
    {'aut_label': '6A', 'centralizer': '110.f1.a1', 'counter': 10, 'group_counter': 15, 'group_order': 3960, 'label': '6A', 'order': 6, 'powers': [5, 3, 10, 10], 'representative': 4098145923, 'size': 110}
  • id: 110096708
    {'aut_label': '6B', 'centralizer': '110.a1.a1', 'counter': 11, 'group_counter': 15, 'group_order': 3960, 'label': '6B', 'order': 6, 'powers': [6, 3, 11, 11], 'representative': 41968373904, 'size': 110}
  • id: 110096709
    {'aut_label': '6C', 'centralizer': '220.b1.a1', 'counter': 12, 'group_counter': 15, 'group_order': 3960, 'label': '6C', 'order': 6, 'powers': [7, 3, 12, 12], 'representative': 57979722507, 'size': 220}
  • id: 110096710
    {'aut_label': '6D', 'centralizer': '330.a1.a1', 'counter': 13, 'group_counter': 15, 'group_order': 3960, 'label': '6D', 'order': 6, 'powers': [6, 4, 13, 13], 'representative': 21236831521, 'size': 330}
  • id: 110096711
    {'aut_label': '6E', 'centralizer': '330.a1.a1', 'counter': 14, 'group_counter': 15, 'group_order': 3960, 'label': '6E', 'order': 6, 'powers': [6, 2, 14, 14], 'representative': 10597639829, 'size': 330}
  • id: 110096712
    {'aut_label': '10A1', 'centralizer': '396.a1.a1', 'counter': 15, 'group_counter': 15, 'group_order': 3960, 'label': '10A1', 'order': 10, 'powers': [8, 16, 2, 15], 'representative': 8960007845, 'size': 396}
  • id: 110096713
    {'aut_label': '10A3', 'centralizer': '396.a1.a1', 'counter': 16, 'group_counter': 15, 'group_order': 3960, 'label': '10A3', 'order': 10, 'powers': [9, 15, 2, 16], 'representative': 53935703309, 'size': 396}
  • id: 110096714
    {'aut_label': '11A1', 'centralizer': '60.a1.a1', 'counter': 17, 'group_counter': 15, 'group_order': 3960, 'label': '11A1', 'order': 11, 'powers': [18, 17, 17, 1], 'representative': 7041527280, 'size': 60}
  • id: 110096715
    {'aut_label': '11A1', 'centralizer': '60.a1.a1', 'counter': 18, 'group_counter': 15, 'group_order': 3960, 'label': '11A-1', 'order': 11, 'powers': [17, 18, 18, 1], 'representative': 37382290824, 'size': 60}
  • id: 110096716
    {'aut_label': '15A1', 'centralizer': '264.a1.a1', 'counter': 19, 'group_counter': 15, 'group_order': 3960, 'label': '15A1', 'order': 15, 'powers': [20, 8, 5, 19], 'representative': 46118461804, 'size': 264}
  • id: 110096718
    {'aut_label': '15A2', 'centralizer': '264.a1.a1', 'counter': 20, 'group_counter': 15, 'group_order': 3960, 'label': '15A2', 'order': 15, 'powers': [19, 9, 5, 20], 'representative': 63432928323, 'size': 264}
  • id: 110096719
    {'aut_label': '22A1', 'centralizer': '180.a1.a1', 'counter': 21, 'group_counter': 15, 'group_order': 3960, 'label': '22A1', 'order': 22, 'powers': [17, 21, 21, 2], 'representative': 28036608725, 'size': 180}
  • id: 110096720
    {'aut_label': '22A1', 'centralizer': '180.a1.a1', 'counter': 22, 'group_counter': 15, 'group_order': 3960, 'label': '22A-1', 'order': 22, 'powers': [18, 22, 22, 2], 'representative': 58224186725, 'size': 180}
  • id: 110096721
    {'aut_label': '33A1', 'centralizer': '120.a1.a1', 'counter': 23, 'group_counter': 15, 'group_order': 3960, 'label': '33A1', 'order': 33, 'powers': [24, 18, 23, 5], 'representative': 27597886828, 'size': 120}
  • id: 110096722
    {'aut_label': '33A1', 'centralizer': '120.a1.a1', 'counter': 24, 'group_counter': 15, 'group_order': 3960, 'label': '33A-1', 'order': 33, 'powers': [23, 17, 24, 5], 'representative': 65808369483, 'size': 120}
• 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: 4517885
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.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], 'schur_index': 1}
  • id: 4517895
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.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], 'schur_index': 1}
  • id: 4517896
    {'cdim': 2, 'counter': 3, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, -1, 2, -1, 2, 2, -1, 2, -1, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4517897
    {'cdim': 5, 'counter': 4, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.5a', 'multiplicity': 2, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 10, -2, -2, 0, 0, 2, 2, 2, 2, -2, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4517898
    {'cdim': 5, 'counter': 5, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.5b', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, -10, 2, -2, 10, -2, -2, 0, 0, 2, 2, 2, -2, 2, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4517899
    {'cdim': 10, 'counter': 6, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.10a', 'multiplicity': 1, 'nt': [11, 5], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 10, 1, 1, 0, 0, 2, -1, -1, -1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4517900
    {'cdim': 10, 'counter': 7, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.10b', 'multiplicity': 1, 'nt': [22, 13], 'qdim': 10, 'qvalues': [10, -10, 2, -2, 10, 1, 1, 0, 0, 2, -1, -1, 1, -1, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4517901
    {'cdim': 10, 'counter': 8, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.10c', 'multiplicity': 1, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, 10, -2, -2, 10, 1, 1, 0, 0, -2, 1, 1, 1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4517902
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.10d', 'multiplicity': 1, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, -10, -2, 2, 10, 1, 1, 0, 0, -2, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4517887
    {'cdim': 11, 'counter': 11, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.11a', 'multiplicity': 1, 'nt': [12, 179], 'qdim': 11, 'qvalues': [11, 11, -1, -1, 11, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4517888
    {'cdim': 11, 'counter': 12, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.11b', 'multiplicity': 1, 'nt': [24, 2948], 'qdim': 11, 'qvalues': [11, -11, -1, 1, 11, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4517886
    {'cdim': 10, 'counter': 10, 'faithful': True, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.10e', 'multiplicity': 2, 'nt': [165, 0], 'qdim': 20, 'qvalues': [20, 0, 4, 0, -10, -4, 2, 0, 0, -2, 4, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4517891
    {'cdim': 20, 'counter': 15, 'faithful': True, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.20a', 'multiplicity': 1, 'nt': [33, 22], 'qdim': 20, 'qvalues': [20, 0, 4, 0, -10, 2, -1, 0, 0, -2, -2, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4517892
    {'cdim': 20, 'counter': 16, 'faithful': True, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.20b', 'multiplicity': 1, 'nt': [165, 0], 'qdim': 20, 'qvalues': [20, 0, -4, 0, -10, 2, -1, 0, 0, 2, 2, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4517893
    {'cdim': 22, 'counter': 17, 'faithful': True, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.22a', 'multiplicity': 1, 'nt': [36, 4977], 'qdim': 22, 'qvalues': [22, 0, -2, 0, -11, -2, 1, 2, 2, 1, -2, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4517889
    {'cdim': 12, 'counter': 13, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.12a', 'multiplicity': 2, 'nt': [55, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 24, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4517890
    {'cdim': 12, 'counter': 14, 'faithful': False, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.12b', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 24, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1, 2, 2, -1, -1, -2, -2, 2, 2], 'schur_index': 1}
  • id: 4517894
    {'cdim': 24, 'counter': 18, 'faithful': True, 'group': '3960.o', 'group_order': 3960, 'image': None, 'label': '3960.o.24a', 'multiplicity': 2, 'nt': [165, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -24, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 1, 1, 0, 0, -2, -2], '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: 7004165
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 3960, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 3960, 'label': '3960.o.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]]]}
  • id: 7004176
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 3960, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1980, 'label': '3960.o.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]]]}
  • id: 7004182
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 660, 'counter': 3, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 660, 'label': '3960.o.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004183
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 4, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 0, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.5a1', 'nt': [55, 0], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7004184
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 5, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 0, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.5a2', 'nt': [55, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7004185
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 6, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.5b1', 'nt': [110, 0], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7004186
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 7, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.5b2', 'nt': [110, 2], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7004187
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 8, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.10a', 'nt': [11, 5], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004188
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 9, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.10b', 'nt': [22, 13], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004166
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 10, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.10c', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-2, 0]], [[-2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004167
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 11, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.10d', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004168
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 0, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.10e1', 'nt': [165, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-5, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7004169
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [3, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 0, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.10e2', 'nt': [165, 2], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-5, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7004170
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 14, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.11a', 'nt': [12, 179], 'q_character': None, 'values': [[[11, 0]], [[11, 0]], [[-1, 0]], [[-1, 0]], [[11, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7004171
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 15, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.11b', 'nt': [24, 2948], 'q_character': None, 'values': [[[11, 0]], [[-11, 0]], [[-1, 0]], [[1, 0]], [[11, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7004172
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 16, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.12a1', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004173
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 17, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1.a1', 'kernel_order': 6, 'label': '3960.o.12a2', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004174
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 18, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.12b1', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004175
    {'center': '660.a1.a1', 'center_index': 660, 'center_order': 6, 'counter': 19, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 3, 'label': '3960.o.12b2', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004177
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 1, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.20a', 'nt': [33, 22], 'q_character': None, 'values': [[[20, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004178
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 1, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.20b', 'nt': [165, 0], 'q_character': None, 'values': [[[20, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7004179
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 22, 'faithful': True, 'field': [0, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 1, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.22a', 'nt': [36, 4977], 'q_character': None, 'values': [[[22, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-11, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7004180
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 1, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.24a1', 'nt': [165, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7004181
    {'center': '3960.a1.a1', 'center_index': 3960, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '3960.o', 'group_counter': 15, 'group_order': 3960, 'image': None, 'image_isoclass': '3960.o', 'image_order': 3960, 'indicator': 1, 'kernel': '3960.a1.a1', 'kernel_order': 1, 'label': '3960.o.24a2', 'nt': [165, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 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: 66319520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3960, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 330, 'label': '3960.o.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': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3960.o', 'subgroup_hash': 6655759197249528573, 'subgroup_order': 3960, 'subgroup_tex': 'S_3\\times \\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 66319531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1980, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3960.o.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': False, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1980.57', 'subgroup_hash': 57, 'subgroup_order': 1980, 'subgroup_tex': 'C_3\\times \\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 66319542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 660, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1320.134', 'subgroup_hash': 134, 'subgroup_order': 1320, 'subgroup_tex': 'C_2\\times \\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 66319553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 660, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3960.o.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['PC', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '660.13', 'subgroup_hash': 13, 'subgroup_order': 660, 'subgroup_tex': '\\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 66319564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '3960.o.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '3960.o.11.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319586
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.12.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '330.2', 'subgroup_hash': 2, 'subgroup_order': 330, 'subgroup_tex': 'C_{33}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66319597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 66319607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.22.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 66319521
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 66319522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.33.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.a1.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319524
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66319525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '3960.o.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66319526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '3960.o.55.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66319527
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 6, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 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': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 66319528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': 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: 66319529
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.66.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.b1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.66.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.b1.a2', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66319532
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 55, 'label': '3960.o.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 66319533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66319535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.b1.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66319536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66319538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66319539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66319540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.110.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 33, 'characteristic': False, 'core_order': 3, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 66319543
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 66319544
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 66319545
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 66319546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.165.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.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': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66319547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.165.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.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': 165, 'quotient_simple': 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: 66319548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.165.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.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': 165, 'quotient_simple': 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: 66319549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 66319550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.198.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 66319551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66319554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.c1.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.220.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319559
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 66319560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.b1.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': 330, 'quotient_simple': 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: 66319563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.g1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.g1.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': 330, 'quotient_simple': 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: 66319570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66319572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66319573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.330.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '330.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': 330, 'quotient_simple': 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: 66319574
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '3960.o.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 66319576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.396.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 66319577
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.396.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 66319578
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.396.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 66319579
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '3960.o.440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 66319580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '3960.o.495.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '495.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': 495, 'quotient_simple': 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': 2}
  • id: 66319581
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': True, 'centralizer_order': 660, 'characteristic': True, 'core_order': 6, 'counter': 65, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3960.o.660.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '660.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '660.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 660, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,11)', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319582
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.660.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.660.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.660.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.660.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319587
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319588
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': 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: 66319589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.660.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319591
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319592
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319593
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': 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: 66319594
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.660.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.j1.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': 660, 'quotient_simple': 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: 66319595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '3960.o.792.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 66319596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.990.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '990.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': 990, 'quotient_simple': 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: 66319598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.990.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '990.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': 990, 'quotient_simple': 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: 66319599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3960.o.990.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '990.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': 990, 'quotient_simple': 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: 66319600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1980, 'characteristic': True, 'core_order': 3, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3960.o.1320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1320.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1320.134', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 134, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1320, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\PSL(2,11)', 'simple': True, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319601
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.1320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.1320.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66319603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1320, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.1980.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1980.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': 1980, '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: 66319604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.1980.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1980.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': 1980, '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: 66319605
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3960.o.1980.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1980.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': 1980, '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: 66319606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': True, 'central_factor': False, 'centralizer_order': 3960, 'characteristic': True, 'core_order': 1, 'counter': 88, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '3960.o.3960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3960.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '3960.o', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6655759197249528573, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3960, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times \\PSL(2,11)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'C3'], '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: 66319520
    {'ambient': '3960.o', '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': '3960.a1.a1', 'complements': ['3960.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '11.a1.a1', '11.a1.a2', '12.a1.a1', '55.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4403, 5324, 7363, 4954, 4154, 3680, 3950, 3680], 'generators': [4, 21755830320, 5, 3369392666], 'label': '3960.o.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '660.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '3960.o', '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': '3960.o'}
  • id: 66319521
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '220.7', 'aut_weyl_index': 36, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '12.a1.a1'], 'contains': ['72.a1.a1', '120.a1.a1', '264.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1413, -1, 8447, -1, 1018, -1, 876, -1], 'generators': [48234212668, 4, 6785983587], 'label': '3960.o.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '3960.o', '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': '110.2'}
  • id: 66319522
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '60.5', 'aut_weyl_index': 132, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.b1.a1', '165.a1.a1', '198.a1.a1', '330.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': '33T22', 'count': 33, 'diagramx': [4016, -1, 7560, -1, 3934, -1, 2932, -1], 'generators': [6230740320, 1, 958126321], 'label': '3960.o.33.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 66319523
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '60.5', 'aut_weyl_index': 132, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a2'], 'contains': ['66.b1.a2', '165.a1.a1', '198.a1.a1', '330.b1.a2'], 'core': '3960.a1.a1', 'coset_action_label': '33T22', 'count': 33, 'diagramx': [4016, -1, 7054, -1, 3934, -1, 3677, -1], 'generators': [31942891704, 1, 24951690985], 'label': '3960.o.33.a1.a2', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a2', 'old_label': '33.a1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a2', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 66319524
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '110.1', 'aut_weyl_index': 72, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '12.a1.a1'], 'contains': ['72.a1.a1', '180.a1.a1', '396.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': '36T4977', 'count': 36, 'diagramx': [1052, -1, 8887, -1, 318, -1, 273, -1], 'generators': [48234212666, 2, 6785983586], 'label': '3960.o.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
  • id: 66319525
    {'ambient': '3960.o', 'aut_centralizer_order': 1, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '144.183', 'aut_weyl_index': 55, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.a1.a2'], 'contains': ['110.e1.a1', '165.a1.a1', '165.c1.a1', '220.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3277, -1, 8610, -1, 5049, -1, 4935, -1], 'generators': [12936673682, 4, 5, 25470589082, 19160161228], 'label': '3960.o.55.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 66319526
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '72.46', 'aut_weyl_index': 110, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['110.a1.a1', '110.b1.a1', '110.b1.a2', '110.c1.a1', '110.d1.a1', '110.d1.a2', '110.f1.a1', '165.b1.a1', '165.c1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6703, -1, 3396, -1, 7070, -1, 6453, -1], 'generators': [27068756404, 20197986504, 4, 21755830320, 5], 'label': '3960.o.55.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '55.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319527
    {'ambient': '3960.o', 'aut_centralizer_order': 11, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '60.11', 'aut_weyl_index': 132, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['120.a1.a1', '180.a1.a1', '660.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [229, -1, 9918, -1, 1660, -1, 1429, -1], 'generators': [4, 5, 48234212665], 'label': '3960.o.60.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.1'}
  • id: 66319603
    {'ambient': '3960.o', 'aut_centralizer_order': 2640, 'aut_label': '1980.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7920, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '396.a1.a1', '660.a1.a1', '660.b1.a1', '990.a1.a1'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2206, -1, 9127, -1, 4089, -1, 4882, -1], 'generators': [5], 'label': '3960.o.1980.a1.a1', 'mobius_quo': None, 'mobius_sub': -660, 'normal_closure': '660.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '1980.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1980.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319528
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '60.8', 'aut_weyl_index': 132, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.a1.a2'], 'contains': ['132.a1.a1', '132.b1.a1', '132.c1.a1', '198.a1.a1', '330.c1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2418, -1, 9161, -1, 3331, -1, 2516, -1], 'generators': [13412257345, 7268587948, 4, 5], 'label': '3960.o.66.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 66319529
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '66.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '60.5', 'aut_weyl_index': 132, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['330.i1.a1', '396.b1.a1', '660.f1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4314, -1, 6569, -1, 3843, -1, 3311, -1], 'generators': [6230740320, 958126320], 'label': '3960.o.66.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 66319530
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '66.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '60.5', 'aut_weyl_index': 132, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.a1.a2', '33.a1.a2'], 'contains': ['330.i1.a1', '396.b1.a1', '660.f1.a2'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4314, -1, 5414, -1, 3843, -1, 4075, -1], 'generators': [31942891704, 24951690984], 'label': '3960.o.66.b1.a2', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a2', 'old_label': '66.b1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.b1.a2', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 66319531
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2640.a', 'aut_weyl_index': 3, 'centralizer': '1320.a1.a1', 'complements': ['1980.c1.a1', '1980.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '22.a1.a1', '22.a1.a2', '24.a1.a1', '110.f1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4824, 3083, 6380, 8081, 4807, 6321, 4233, 6321], 'generators': [4, 21755830320, 3369392667], 'label': '3960.o.2.a1.a1', 'mobius_quo': 1, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '1320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '3960.o', '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': '1320.134'}
  • id: 66319532
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 72, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '24.a1.a1', '36.a1.a1'], 'contains': ['360.a1.a1', '792.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1119, -1, 8069, -1, 1018, -1, 876, -1], 'generators': [48234212664, 6785983584], 'label': '3960.o.72.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
  • id: 66319533
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '110.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '660.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.a1.a1', '220.b1.a1', '220.d1.a1', '330.a1.a1', '330.c1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7287, -1, 2875, -1, 7654, -1, 6820, -1], 'generators': [27068756404, 20197986504, 4, 5], 'label': '3960.o.110.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319534
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '55.b1.a1'], 'contains': ['220.a1.a1', '220.c1.a1', '220.e1.a1', '330.b1.a1', '330.c1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5014, -1, 6830, -1, 7264, -1, 5693, -1], 'generators': [6267145224, 4, 5, 43643667], 'label': '3960.o.110.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319535
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a2', '55.b1.a1'], 'contains': ['220.a1.a1', '220.c1.a2', '220.e1.a2', '330.b1.a2', '330.c1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5014, -1, 5067, -1, 7264, -1, 6363, -1], 'generators': [6310500720, 4, 5, 31343056804], 'label': '3960.o.110.b1.a2', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.b1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319536
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '72.46', 'aut_weyl_index': 110, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.b1.a1', '220.e1.a1', '220.e1.a2', '330.d1.a1', '330.e1.a1', '330.f1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8647, -1, 1169, -1, 8654, -1, 9152, -1], 'generators': [27068756404, 21755830325, 20197986504, 4], 'label': '3960.o.110.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319537
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.c1.a1', '220.d1.a1', '220.e1.a2', '330.d1.a1', '330.g1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7949, -1, 1847, -1, 8152, -1, 8202, -1], 'generators': [27068756404, 20197986509, 21755830325, 4], 'label': '3960.o.110.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.d1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319538
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.c1.a2', '220.d1.a1', '220.e1.a1', '330.d1.a1', '330.g1.a2'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7949, -1, 2334, -1, 8152, -1, 8599, -1], 'generators': [27068756404, 20197986509, 4, 21755830320], 'label': '3960.o.110.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.d1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319539
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '48.48', 'aut_weyl_index': 165, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.a1.a2', '55.a1.a1'], 'contains': ['330.h1.a1', '330.i1.a1', '330.j1.a1', '440.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5356, -1, 5895, -1, 4847, -1, 4398, -1], 'generators': [25470589083, 4, 12936673683, 19160161228], 'label': '3960.o.110.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '110.e1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66319540
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '110.f1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '24.14', 'aut_weyl_index': 330, 'centralizer': '660.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '55.b1.a1'], 'contains': ['220.b1.a1', '220.c1.a1', '220.c1.a2', '330.h1.a1', '330.k1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5996, -1, 3852, -1, 6875, -1, 6028, -1], 'generators': [27068756404, 20197986504, 4, 21755830320], 'label': '3960.o.110.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.f1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319541
    {'ambient': '3960.o', 'aut_centralizer_order': 33, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.5', 'aut_weyl_index': 396, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.a1.a1'], 'contains': ['360.a1.a1', '1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [668, -1, 9928, -1, 1844, -1, 1587, -1], 'generators': [48234212668, 4], 'label': '3960.o.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '3960.o', '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': '10.2'}
  • id: 66319542
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1320.133', 'aut_weyl_index': 6, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '33.a1.a1', '33.a1.a2', '36.a1.a1', '165.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4403, -1, 7054, -1, 3500, -1, 3109, -1], 'generators': [21755830320, 2, 3369392666], 'label': '3960.o.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': '3960.o', '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': '660.13'}
  • id: 66319543
    {'ambient': '3960.o', 'aut_centralizer_order': 10, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '792.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '66.a1.a1'], 'contains': ['264.a1.a1', '396.a1.a1', '660.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1386, -1, 9726, -1, 2198, -1, 1891, -1], 'generators': [7268587948, 4, 5], 'label': '3960.o.132.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319544
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '132.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '20.4', 'aut_weyl_index': 396, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.a1.a2', '66.a1.a1'], 'contains': ['264.a1.a1', '396.b1.a1', '660.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2352, -1, 7976, -1, 3331, -1, 2866, -1], 'generators': [13412257348, 7268587948, 4], 'label': '3960.o.132.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 66319545
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '132.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '60.8', 'aut_weyl_index': 132, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.a1.a1'], 'contains': ['264.a1.a1', '396.c1.a1', '660.h1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2954, -1, 9118, -1, 2923, -1, 2239, -1], 'generators': [13412257345, 7268587948, 4], 'label': '3960.o.132.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 66319546
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '24.12', 'aut_weyl_index': 330, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a1', '33.a1.a2', '55.a1.a1'], 'contains': ['330.i1.a1', '495.a1.a1', '660.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [3503, -1, 7669, -1, 4219, -1, 3634, -1], 'generators': [19160161224, 12936673682, 2, 25470589082], 'label': '3960.o.165.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1.a1', 'old_label': '165.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66319547
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '165.b1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '55.b1.a1'], 'contains': ['330.a1.a1', '330.b1.a1', '330.b1.a2', '330.e1.a1', '330.g1.a1', '330.g1.a2', '330.k1.a1', '495.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [6786, -1, 3365, -1, 6074, -1, 7273, -1], 'generators': [27068756400, 20197986504, 21755830320, 5], 'label': '3960.o.165.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '165.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319548
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '165.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '990.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.b1.a1'], 'contains': ['330.c1.a1', '330.d1.a1', '330.h1.a1', '495.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4446, -1, 6572, -1, 5511, -1, 4851, -1], 'generators': [12936673682, 4, 5, 25470589082], 'label': '3960.o.165.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '165.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 66319549
    {'ambient': '3960.o', 'aut_centralizer_order': 22, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '10.2', 'aut_weyl_index': 792, 'centralizer': '180.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.a1.a1'], 'contains': ['360.a1.a1', '1980.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [286, -1, 9487, -1, 1527, -1, 1314, -1], 'generators': [1, 48234212665], 'label': '3960.o.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 66319550
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '198.a1', 'aut_quo_index': None, 'aut_stab_index': 198, 'aut_weyl_group': '10.1', 'aut_weyl_index': 792, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a1', '33.a1.a2', '66.a1.a1'], 'contains': ['396.a1.a1', '396.b1.a1', '396.c1.a1', '990.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [1971, -1, 8407, -1, 2602, -1, 2516, -1], 'generators': [7268587944, 1, 13412257345], 'label': '3960.o.198.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '198.a1.a1', 'old_label': '198.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66319551
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '660.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '110.a1.a1', '110.b1.a1', '110.b1.a2'], 'contains': ['440.a1.a1', '660.a1.a1', '660.b1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [2951, -1, 6961, -1, 7470, -1, 5572, -1], 'generators': [4, 5, 19160161228], 'label': '3960.o.220.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319552
    {'ambient': '3960.o', 'aut_centralizer_order': 36, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1980, 'centralizer': '220.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '110.c1.a1', '110.f1.a1'], 'contains': ['440.a1.a1', '660.c1.a1', '660.d1.a1', '660.e1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7547, -1, 2810, -1, 8708, -1, 7705, -1], 'generators': [27068756404, 20197986504, 4], 'label': '3960.o.220.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66319553
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1320.133', 'aut_weyl_index': 6, 'centralizer': '660.a1.a1', 'complements': ['660.a1.a1', '660.h1.a1', '660.j1.a1', '660.j1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['66.b1.a1', '66.b1.a2', '72.a1.a1', '330.k1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4615, 3083, 6116, 8081, 3500, 6321, 3304, 6321], 'generators': [21755830320, 3369392664], 'label': '3960.o.6.a1.a1', 'mobius_quo': -1, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['3960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '660.13'}
  • id: 66319554
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '220.c1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '660.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '110.b1.a1', '110.d1.a1', '110.f1.a1'], 'contains': ['440.a1.a1', '660.c1.a1', '660.f1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6273, -1, 4645, -1, 7957, -1, 6441, -1], 'generators': [6267145224, 4, 43643667], 'label': '3960.o.220.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319555
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '220.c1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '660.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a2', '110.b1.a2', '110.d1.a2', '110.f1.a1'], 'contains': ['440.a1.a1', '660.c1.a1', '660.f1.a2'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6273, -1, 4287, -1, 7957, -1, 6860, -1], 'generators': [6310500720, 4, 31343056804], 'label': '3960.o.220.c1.a2', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.c1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.c1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319556
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '220.d1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '660.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '110.d1.a1', '110.d1.a2'], 'contains': ['440.a1.a1', '660.g1.a1', '660.h1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7978, -1, 2307, -1, 9199, -1, 8127, -1], 'generators': [27068756404, 20197986509, 4], 'label': '3960.o.220.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.d1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66319557
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '220.e1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.b1.a1', '110.c1.a1', '110.d1.a2'], 'contains': ['440.a1.a1', '660.h1.a1', '660.i1.a1', '660.j1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8736, -1, 1675, -1, 9607, -1, 9661, -1], 'generators': [6267145229, 4, 43643667], 'label': '3960.o.220.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.e1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319558
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '220.e1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '36.10', 'aut_weyl_index': 220, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.b1.a2', '110.c1.a1', '110.d1.a1'], 'contains': ['440.a1.a1', '660.h1.a1', '660.i1.a2', '660.j1.a2'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8736, -1, 1068, -1, 9607, -1, 9152, -1], 'generators': [4, 31343056804, 6310500725], 'label': '3960.o.220.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.e1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.e1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66319559
    {'ambient': '3960.o', 'aut_centralizer_order': 30, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1980, 'centralizer': '264.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1'], 'contains': ['792.a1.a1', '1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1994, -1, 9116, -1, 2880, -1, 2267, -1], 'generators': [7268587948, 4], 'label': '3960.o.264.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66319560
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '330.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '330.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '165.b1.a1'], 'contains': ['660.b1.a1', '660.d1.a1', '660.g1.a1', '990.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [6415, -1, 3080, -1, 6323, -1, 7283, -1], 'generators': [27068756400, 20197986504, 5], 'label': '3960.o.330.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319561
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.b1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a1', '110.b1.a1', '165.b1.a1'], 'contains': ['660.b1.a1', '660.f1.a1', '660.i1.a1', '990.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [5394, -1, 7238, -1, 5947, -1, 4789, -1], 'generators': [6267145224, 43643664, 5], 'label': '3960.o.330.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319562
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.b1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a2', '110.b1.a2', '165.b1.a1'], 'contains': ['660.b1.a1', '660.f1.a2', '660.i1.a2', '990.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [5394, -1, 5168, -1, 5947, -1, 6118, -1], 'generators': [6310500720, 31343056800, 5], 'label': '3960.o.330.b1.a2', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.b1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.b1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319563
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '330.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '330.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.a1.a1', '110.a1.a1', '110.b1.a1', '110.b1.a2', '165.c1.a1'], 'contains': ['660.a1.a1', '660.c1.a1', '660.h1.a1', '990.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4088, -1, 6849, -1, 5688, -1, 5248, -1], 'generators': [12936673682, 4, 5], 'label': '3960.o.330.c1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '330.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319564
    {'ambient': '3960.o', 'aut_centralizer_order': 1, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '360.121', 'aut_weyl_index': 22, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '33.a1.a1', '55.a1.a1', '66.a1.a1', '110.b1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3981, -1, 8556, -1, 4154, -1, 3671, -1], 'generators': [958126321, 4, 5, 6230740323], 'label': '3960.o.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 66319565
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.d1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '990.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '110.d1.a1', '110.d1.a2', '165.c1.a1'], 'contains': ['660.c1.a1', '660.h1.a1', '990.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7213, -1, 1028, -1, 8333, -1, 8674, -1], 'generators': [12936673682, 4, 25470589082], 'label': '3960.o.330.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.c1.a1', 'old_label': '330.d1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319566
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.e1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '165.b1.a1'], 'contains': ['660.d1.a1', '660.i1.a1', '660.i1.a2', '990.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [9128, -1, 1561, -1, 6958, -1, 9407, -1], 'generators': [27068756400, 21755830325, 20197986504], 'label': '3960.o.330.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.e1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319567
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '330.f1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1'], 'contains': ['660.e1.a1', '660.j1.a1', '660.j1.a2', '990.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9616, -1, 174, -1, 9903, -1, 9916, -1], 'generators': [27068756404, 21755830325, 20197986504], 'label': '3960.o.330.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '330.f1.a1', 'old_label': '330.f1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319568
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.g1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.d1.a1', '165.b1.a1'], 'contains': ['660.f1.a1', '660.g1.a1', '660.i1.a2', '990.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8364, -1, 2005, -1, 6698, -1, 8450, -1], 'generators': [27068756400, 20197986509, 21755830325], 'label': '3960.o.330.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.g1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319569
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '330.g1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.d1.a2', '165.b1.a1'], 'contains': ['660.f1.a2', '660.g1.a1', '660.i1.a1', '990.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8364, -1, 2589, -1, 6698, -1, 8898, -1], 'generators': [27068756400, 20197986509, 21755830320], 'label': '3960.o.330.g1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '330.g1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.g1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319570
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '330.h1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '330.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.a1', '110.f1.a1', '165.c1.a1'], 'contains': ['660.c1.a1', '990.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3471, -1, 5938, -1, 5052, -1, 4211, -1], 'generators': [25470589083, 4, 12936673683], 'label': '3960.o.330.h1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '330.h1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66319571
    {'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '330.i1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '24.12', 'aut_weyl_index': 330, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.b1.a1', '66.b1.a2', '110.e1.a1', '165.a1.a1'], 'contains': ['990.c1.a1', '1320.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4675, -1, 6228, -1, 3847, -1, 3429, -1], 'generators': [19160161224, 12936673680, 25470589080], 'label': '3960.o.330.i1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '330.i1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66319572
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '330.j1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '24.12', 'aut_weyl_index': 330, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.a1'], 'contains': ['990.c1.a1', '1320.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [6986, -1, 5431, -1, 4107, -1, 3652, -1], 'generators': [12936673680, 19160161228, 25470589080], 'label': '3960.o.330.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.e1.a1', 'old_label': '330.j1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66319573
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '330.k1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 660, 'centralizer': '330.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '110.f1.a1', '165.b1.a1'], 'contains': ['660.d1.a1', '660.f1.a1', '660.f1.a2', '990.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5965, -1, 3895, -1, 5428, -1, 5894, -1], 'generators': [27068756400, 20197986504, 21755830320], 'label': '3960.o.330.k1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '330.k1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319574
    {'ambient': '3960.o', 'aut_centralizer_order': 66, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 792, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.a1.a1', '180.a1.a1'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [507, -1, 9689, -1, 1685, -1, 1450, -1], 'generators': [48234212664], 'label': '3960.o.360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 66319575
    {'ambient': '3960.o', 'aut_centralizer_order': 1, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '360.121', 'aut_weyl_index': 22, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a2', '33.a1.a2', '55.a1.a1', '66.a1.a1', '110.b1.a2'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3981, -1, 7417, -1, 4154, -1, 4795, -1], 'generators': [24951690985, 4, 5, 31942891708], 'label': '3960.o.11.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a2', 'old_label': '11.a1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a2', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 66319576
    {'ambient': '3960.o', 'aut_centralizer_order': 20, 'aut_label': '396.a1', 'aut_quo_index': None, 'aut_stab_index': 198, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '396.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '132.a1.a1', '198.a1.a1'], 'contains': ['792.a1.a1', '1980.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [1189, -1, 8812, -1, 2562, -1, 1994, -1], 'generators': [7268587944, 5], 'label': '3960.o.396.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '198.a1.a1', 'old_label': '396.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319577
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '396.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '10.1', 'aut_weyl_index': 792, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.b1.a1', '66.b1.a2', '132.b1.a1', '198.a1.a1'], 'contains': ['792.a1.a1', '1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1991, -1, 7957, -1, 3688, -1, 3003, -1], 'generators': [7268587944, 13412257344], 'label': '3960.o.396.b1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '396.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66319578
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '396.c1', 'aut_quo_index': None, 'aut_stab_index': 198, 'aut_weyl_group': '10.1', 'aut_weyl_index': 792, 'centralizer': '1980.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.c1.a1', '198.a1.a1'], 'contains': ['792.a1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [2976, -1, 8362, -1, 3428, -1, 2516, -1], 'generators': [7268587944, 13412257345], 'label': '3960.o.396.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '198.a1.a1', 'old_label': '396.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 66319579
    {'ambient': '3960.o', 'aut_centralizer_order': 36, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1980, 'centralizer': '220.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.a1', '220.a1.a1', '220.b1.a1', '220.c1.a1', '220.c1.a2', '220.d1.a1', '220.e1.a1', '220.e1.a2'], 'contains': ['1320.a1.a1', '1320.b1.a1', '1320.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7629, -1, 4164, -1, 7524, -1, 6860, -1], 'generators': [4, 19160161228], 'label': '3960.o.440.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '440.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66319580
    {'ambient': '3960.o', 'aut_centralizer_order': 8, 'aut_label': '495.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '495.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['165.a1.a1', '165.b1.a1', '165.c1.a1'], 'contains': ['990.a1.a1', '990.b1.a1', '990.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [4789, -1, 6716, -1, 4659, -1, 4550, -1], 'generators': [12936673682, 2, 25470589082], 'label': '3960.o.495.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1.a1', 'old_label': '495.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '495.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66319581
    {'ambient': '3960.o', 'aut_centralizer_order': 1320, 'aut_label': '660.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '6.a1.a1', 'complements': ['6.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '132.a1.a1', '220.a1.a1', '330.c1.a1'], 'contains': ['1320.a1.a1', '1980.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2197, 6917, 9116, 1919, 3168, 1039, 4295, 1039], 'generators': [4, 5], 'label': '3960.o.660.a1.a1', 'mobius_quo': 0, 'mobius_sub': 660, 'normal_closure': '660.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['1320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '660.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': '1.1', 'quotient_action_kernel': '660.13', 'quotient_action_kernel_order': 660, 'quotient_fusion': None, 'short_label': '660.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319582
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '660.b1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '330.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['165.a1.a1', '220.a1.a1', '330.a1.a1', '330.b1.a1', '330.b1.a2'], 'contains': ['1320.b1.a1', '1980.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [3116, -1, 7001, -1, 5341, -1, 5572, -1], 'generators': [19160161224, 5], 'label': '3960.o.660.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '660.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319583
    {'ambient': '3960.o', 'aut_centralizer_order': 72, 'aut_label': '660.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '110.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.b1.a1', '220.b1.a1', '220.c1.a1', '220.c1.a2', '330.c1.a1', '330.d1.a1', '330.h1.a1'], 'contains': ['1320.a1.a1', '1980.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3841, -1, 5640, -1, 5861, -1, 6248, -1], 'generators': [4, 12936673683], 'label': '3960.o.660.c1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319584
    {'ambient': '3960.o', 'aut_centralizer_order': 72, 'aut_label': '660.d1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '110.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.b1.a1', '330.a1.a1', '330.e1.a1', '330.k1.a1'], 'contains': ['1320.b1.a1', '1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [7021, -1, 3160, -1, 6121, -1, 7193, -1], 'generators': [27068756400, 20197986504], 'label': '3960.o.660.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.d1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319585
    {'ambient': '3960.o', 'aut_centralizer_order': 36, 'aut_label': '660.e1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '220.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.b1.a1', '330.f1.a1'], 'contains': ['1320.c1.a1', '1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [9476, -1, 490, -1, 8282, -1, 8991, -1], 'generators': [27068756404, 20197986504], 'label': '3960.o.660.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.c1.a1', 'old_label': '660.e1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319586
    {'ambient': '3960.o', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.15', 'aut_weyl_index': 12, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '60.a1.a1', '132.a1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1293, -1, 9612, -1, 1660, -1, 1115, -1], 'generators': [4, 5, 6785983586, 48234212665], 'label': '3960.o.12.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
  • id: 66319587
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '660.f1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '330.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.b1.a1', '220.c1.a1', '330.b1.a1', '330.g1.a1', '330.k1.a1'], 'contains': ['1320.b1.a1', '1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5943, -1, 4673, -1, 5601, -1, 6025, -1], 'generators': [6267145224, 43643664], 'label': '3960.o.660.f1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.f1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319588
    {'ambient': '3960.o', 'aut_centralizer_order': 12, 'aut_label': '660.f1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '330.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.b1.a2', '220.c1.a2', '330.b1.a2', '330.g1.a2', '330.k1.a1'], 'contains': ['1320.b1.a1', '1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5943, -1, 4019, -1, 5601, -1, 6472, -1], 'generators': [6310500720, 31343056800], 'label': '3960.o.660.f1.a2', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.f1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.f1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319589
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '660.g1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '330.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.d1.a1', '330.a1.a1', '330.g1.a1', '330.g1.a2'], 'contains': ['1320.b1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7990, -1, 2654, -1, 6640, -1, 8065, -1], 'generators': [27068756400, 20197986509], 'label': '3960.o.660.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '660.g1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319590
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '660.h1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '330.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.c1.a1', '220.d1.a1', '220.e1.a1', '220.e1.a2', '330.c1.a1', '330.d1.a1'], 'contains': ['1320.a1.a1', '1980.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6665, -1, 2129, -1, 6381, -1, 7842, -1], 'generators': [12936673682, 4], 'label': '3960.o.660.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.h1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319591
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '660.i1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.e1.a1', '330.b1.a1', '330.e1.a1', '330.g1.a2'], 'contains': ['1320.b1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8888, -1, 2427, -1, 6900, -1, 8767, -1], 'generators': [6267145229, 43643664], 'label': '3960.o.660.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '660.i1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319592
    {'ambient': '3960.o', 'aut_centralizer_order': 4, 'aut_label': '660.i1', 'aut_quo_index': None, 'aut_stab_index': 330, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.e1.a2', '330.b1.a2', '330.e1.a1', '330.g1.a1'], 'contains': ['1320.b1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8888, -1, 1619, -1, 6900, -1, 8289, -1], 'generators': [31343056800, 6310500725], 'label': '3960.o.660.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '660.i1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.i1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319593
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '660.j1', 'aut_quo_index': None, 'aut_stab_index': 660, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.e1.a1', '330.f1.a1'], 'contains': ['1320.c1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9771, -1, 275, -1, 9101, -1, 9581, -1], 'generators': [6267145229, 43643667], 'label': '3960.o.660.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '330.f1.a1', 'old_label': '660.j1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319594
    {'ambient': '3960.o', 'aut_centralizer_order': 2, 'aut_label': '660.j1', 'aut_quo_index': None, 'aut_stab_index': 660, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '1980.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.e1.a2', '330.f1.a1'], 'contains': ['1320.c1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9771, -1, 72, -1, 9101, -1, 9214, -1], 'generators': [31343056804, 6310500725], 'label': '3960.o.660.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '330.f1.a1', 'old_label': '660.j1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.j1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66319595
    {'ambient': '3960.o', 'aut_centralizer_order': 60, 'aut_label': '792.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '132.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '264.a1.a1', '396.a1.a1', '396.b1.a1', '396.c1.a1'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1658, -1, 8509, -1, 2894, -1, 2391, -1], 'generators': [7268587944], 'label': '3960.o.792.a1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '792.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319596
    {'ambient': '3960.o', 'aut_centralizer_order': 48, 'aut_label': '990.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7920, 'centralizer': '165.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['198.a1.a1', '330.a1.a1', '330.b1.a1', '330.b1.a2', '330.c1.a1', '495.a1.a1'], 'contains': ['1980.a1.a1', '1980.b1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [5201, -1, 7193, -1, 5063, -1, 5248, -1], 'generators': [12936673682, 2], 'label': '3960.o.990.a1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '990.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '990.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319597
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '120.35', 'aut_weyl_index': 66, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['66.b1.a1', '110.e1.a1', '132.b1.a1', '220.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5214, -1, 6516, -1, 4562, -1, 4096, -1], 'generators': [4, 958126324, 6230740323], 'label': '3960.o.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 66319598
    {'ambient': '3960.o', 'aut_centralizer_order': 8, 'aut_label': '990.b1', 'aut_quo_index': None, 'aut_stab_index': 495, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '495.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['330.d1.a1', '330.e1.a1', '330.f1.a1', '330.g1.a1', '330.g1.a2', '495.a1.a1'], 'contains': ['1980.b1.a1', '1980.c1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 495, 'diagramx': [8580, -1, 1431, -1, 7178, -1, 8528, -1], 'generators': [12936673682, 25470589082], 'label': '3960.o.990.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '495.a1.a1', 'old_label': '990.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '990.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319599
    {'ambient': '3960.o', 'aut_centralizer_order': 24, 'aut_label': '990.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1320, 'centralizer': '165.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['330.h1.a1', '330.i1.a1', '330.j1.a1', '330.k1.a1', '495.a1.a1'], 'contains': ['1980.b1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4830, -1, 6074, -1, 4713, -1, 4770, -1], 'generators': [12936673680, 25470589080], 'label': '3960.o.990.c1.a1', 'mobius_quo': None, 'mobius_sub': 9, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '990.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '990.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66319600
    {'ambient': '3960.o', 'aut_centralizer_order': 3960, 'aut_label': '1320.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '264.a1.a1', '440.a1.a1', '660.a1.a1', '660.c1.a1', '660.h1.a1'], 'contains': ['3960.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3100, 5207, 8362, 4669, 5439, 3187, 6025, 3187], 'generators': [4], 'label': '3960.o.1320.a1.a1', 'mobius_quo': -1, 'mobius_sub': -660, 'normal_closure': '1320.a1.a1', 'normal_contained_in': ['2.a1.a1', '660.a1.a1'], 'normal_contains': ['3960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1320.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': '2.1', 'quotient_action_kernel': '660.13', 'quotient_action_kernel_order': 660, 'quotient_fusion': None, 'short_label': '1320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319601
    {'ambient': '3960.o', 'aut_centralizer_order': 72, 'aut_label': '1320.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '110.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['330.i1.a1', '440.a1.a1', '660.b1.a1', '660.d1.a1', '660.f1.a1', '660.f1.a2', '660.g1.a1', '660.i1.a1', '660.i1.a2'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6586, -1, 3767, -1, 6056, -1, 6730, -1], 'generators': [19160161224], 'label': '3960.o.1320.b1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '1320.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319602
    {'ambient': '3960.o', 'aut_centralizer_order': 36, 'aut_label': '1320.c1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3960, 'centralizer': '220.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['330.j1.a1', '440.a1.a1', '660.e1.a1', '660.j1.a1', '660.j1.a2'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [9356, -1, 431, -1, 7524, -1, 8752, -1], 'generators': [19160161228], 'label': '3960.o.1320.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.c1.a1', 'old_label': '1320.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66319604
    {'ambient': '3960.o', 'aut_centralizer_order': 144, 'aut_label': '1980.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7920, 'centralizer': '55.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['396.b1.a1', '660.c1.a1', '660.d1.a1', '660.e1.a1', '660.f1.a1', '660.f1.a2', '990.a1.a1', '990.b1.a1', '990.c1.a1'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5201, -1, 4729, -1, 5698, -1, 6248, -1], 'generators': [12936673680], 'label': '3960.o.1980.b1.a1', 'mobius_quo': None, 'mobius_sub': -54, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '1980.b1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1980.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319605
    {'ambient': '3960.o', 'aut_centralizer_order': 48, 'aut_label': '1980.c1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7920, 'centralizer': '165.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['396.c1.a1', '660.g1.a1', '660.h1.a1', '660.i1.a1', '660.i1.a2', '660.j1.a1', '660.j1.a2', '990.a1.a1', '990.b1.a1'], 'contains': ['3960.a1.a1'], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7547, -1, 2256, -1, 6445, -1, 8177, -1], 'generators': [12936673682], 'label': '3960.o.1980.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.b1.a1', 'old_label': '1980.c1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1980.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319606
    {'ambient': '3960.o', 'aut_centralizer_order': None, 'aut_label': '3960.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': ['360.a1.a1', '792.a1.a1', '1320.a1.a1', '1320.b1.a1', '1320.c1.a1', '1980.a1.a1', '1980.b1.a1', '1980.c1.a1'], 'contains': [], 'core': '3960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4151, 4292, 5565, 6185, 5569, 4736, 6137, 4736], 'generators': [], 'label': '3960.o.3960.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1980, 'normal_closure': '3960.a1.a1', 'normal_contained_in': ['6.a1.a1', '1320.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '3960.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66319607
    {'ambient': '3960.o', 'aut_centralizer_order': 3, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '120.35', 'aut_weyl_index': 66, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a2'], 'contains': ['66.b1.a2', '110.e1.a1', '132.b1.a1', '220.c1.a2'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5214, -1, 5925, -1, 4562, -1, 4515, -1], 'generators': [24951690988, 4, 31942891708], 'label': '3960.o.22.a1.a2', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a2', 'old_label': '22.a1.a2', 'projective_image': '3960.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a2', 'subgroup_fusion': None, 'weyl_group': '120.35'}