Abstract group data - 1440.5848

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [12, 4], 'aut_gens': [[90724, 121098], [131771, 51977], [16683, 82089]], 'aut_group': '2880.dv', 'aut_hash': 409072078557532110, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2880, 'aut_permdeg': 21, 'aut_perms': [14784990563678786683, 5739221403620976386], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 1], [2, 15, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 6, 1, 1], [4, 90, 1, 1], [5, 12, 2, 1], [6, 60, 1, 1], [6, 120, 1, 2], [10, 36, 2, 1], [10, 72, 2, 1], [12, 120, 1, 1], [15, 96, 2, 1], [20, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times S_5', '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': 60, 'autcentquo_group': '2880.dv', 'autcentquo_hash': 409072078557532110, 'autcentquo_nilpotent': False, 'autcentquo_order': 2880, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 6, 1], [2, 15, 1], [2, 45, 1], [2, 90, 1], [3, 8, 1], [3, 20, 1], [3, 160, 1], [4, 6, 1], [4, 90, 1], [5, 12, 2], [6, 60, 1], [6, 120, 2], [10, 36, 2], [10, 72, 2], [12, 120, 1], [15, 96, 2], [20, 72, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '1440.5848', 'commutator_count': 1, 'commutator_label': '720.768', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '60.5'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 5848, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['60.5', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 1], [2, 15, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 6, 1, 1], [4, 90, 1, 1], [5, 12, 2, 1], [6, 60, 1, 1], [6, 120, 1, 2], [10, 36, 2, 1], [10, 72, 2, 1], [12, 120, 1, 1], [15, 96, 2, 1], [20, 72, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 171, 'exponent': 60, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[9, 1, 4], [12, 1, 2], [15, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1440.5848', 'hash': 5848, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [6, 20], 'inner_gens': [[90724, 136937], [177972, 121098]], 'inner_hash': 5848, 'inner_nilpotent': False, 'inner_order': 1440, 'inner_split': True, 'inner_tex': 'S_4\\times A_5', 'inner_used': [1, 2], 'irrC_degree': 9, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 9, 'irrep_stats': [[1, 2], [2, 1], [3, 6], [4, 2], [5, 2], [6, 2], [8, 1], [9, 4], [10, 1], [12, 2], [15, 2]], 'label': '1440.5848', 'linC_count': 8, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 4, 'linQ_dim': 7, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S4*A5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 25, 'number_divisions': 20, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 153, 'number_subgroup_classes': 154, 'number_subgroups': 4298, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 159], [3, 188], [4, 96], [5, 24], [6, 300], [10, 216], [12, 120], [15, 192], [20, 144]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [51120], 'outer_gens': [[40444, 132618]], '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': 9, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [8, 1], [10, 1], [12, 3], [15, 2], [18, 2]], 'representations': {'Perm': {'d': 9, 'gens': [90724, 121098]}}, 'schur_multiplier': [2, 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_4\\times A_5', 'transitive_degree': 20, '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: 108767630
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 5848, 'group_order': 1440, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 108767641
    {'aut_label': '2A', 'centralizer': '3.a1.a1', 'counter': 2, 'group_counter': 5848, 'group_order': 1440, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 23, 'size': 3}
  • id: 108767648
    {'aut_label': '2B', 'centralizer': '6.b1.a1', 'counter': 3, 'group_counter': 5848, 'group_order': 1440, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 14, 'size': 6}
  • id: 108767649
    {'aut_label': '2C', 'centralizer': '15.b1.a1', 'counter': 4, 'group_counter': 5848, 'group_order': 1440, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 41040, 'size': 15}
  • id: 108767650
    {'aut_label': '2D', 'centralizer': '45.a1.a1', 'counter': 5, 'group_counter': 5848, 'group_order': 1440, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 85807, 'size': 45}
  • id: 108767651
    {'aut_label': '2E', 'centralizer': '90.b1.a1', 'counter': 6, 'group_counter': 5848, 'group_order': 1440, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 16686, 'size': 90}
  • id: 108767652
    {'aut_label': '3A', 'centralizer': '8.a1.a1', 'counter': 7, 'group_counter': 5848, 'group_order': 1440, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 20, 'size': 8}
  • id: 108767653
    {'aut_label': '3B', 'centralizer': '20.a1.a1', 'counter': 8, 'group_counter': 5848, 'group_order': 1440, 'label': '3B', 'order': 3, 'powers': [8, 1, 8], 'representative': 15240, 'size': 20}
  • id: 108767654
    {'aut_label': '3C', 'centralizer': '160.a1.a1', 'counter': 9, 'group_counter': 5848, 'group_order': 1440, 'label': '3C', 'order': 3, 'powers': [9, 1, 9], 'representative': 166459, 'size': 160}
  • id: 108767631
    {'aut_label': '4A', 'centralizer': '6.c1.a1', 'counter': 10, 'group_counter': 5848, 'group_order': 1440, 'label': '4A', 'order': 4, 'powers': [2, 10, 10], 'representative': 10, 'size': 6}
  • id: 108767632
    {'aut_label': '4B', 'centralizer': '90.d1.a1', 'counter': 11, 'group_counter': 5848, 'group_order': 1440, 'label': '4B', 'order': 4, 'powers': [2, 11, 11], 'representative': 167890, 'size': 90}
  • id: 108767633
    {'aut_label': '5A1', 'centralizer': '12.b1.a1', 'counter': 12, 'group_counter': 5848, 'group_order': 1440, 'label': '5A1', 'order': 5, 'powers': [13, 13, 1], 'representative': 46800, 'size': 12}
  • id: 108767634
    {'aut_label': '5A1', 'centralizer': '12.b1.a1', 'counter': 13, 'group_counter': 5848, 'group_order': 1440, 'label': '5A2', 'order': 5, 'powers': [12, 12, 1], 'representative': 97320, 'size': 12}
  • id: 108767635
    {'aut_label': '6A', 'centralizer': '60.g1.a1', 'counter': 14, 'group_counter': 5848, 'group_order': 1440, 'label': '6A', 'order': 6, 'powers': [8, 2, 14], 'representative': 6623, 'size': 60}
  • id: 108767636
    {'aut_label': '6B', 'centralizer': '120.b1.a1', 'counter': 15, 'group_counter': 5848, 'group_order': 1440, 'label': '6B', 'order': 6, 'powers': [8, 3, 15], 'representative': 45374, 'size': 120}
  • id: 108767637
    {'aut_label': '6C', 'centralizer': '120.n1.a1', 'counter': 16, 'group_counter': 5848, 'group_order': 1440, 'label': '6C', 'order': 6, 'powers': [7, 4, 16], 'representative': 41060, 'size': 120}
  • id: 108767638
    {'aut_label': '10A1', 'centralizer': '36.e1.a1', 'counter': 17, 'group_counter': 5848, 'group_order': 1440, 'label': '10A1', 'order': 10, 'powers': [13, 18, 2], 'representative': 51976, 'size': 36}
  • id: 108767639
    {'aut_label': '10A1', 'centralizer': '36.e1.a1', 'counter': 18, 'group_counter': 5848, 'group_order': 1440, 'label': '10A3', 'order': 10, 'powers': [12, 17, 2], 'representative': 96496, 'size': 36}
  • id: 108767640
    {'aut_label': '10B1', 'centralizer': '72.a1.a1', 'counter': 19, 'group_counter': 5848, 'group_order': 1440, 'label': '10B1', 'order': 10, 'powers': [12, 20, 3], 'representative': 161281, 'size': 72}
  • id: 108767642
    {'aut_label': '10B1', 'centralizer': '72.a1.a1', 'counter': 20, 'group_counter': 5848, 'group_order': 1440, 'label': '10B3', 'order': 10, 'powers': [13, 19, 3], 'representative': 92161, 'size': 72}
  • id: 108767643
    {'aut_label': '12A', 'centralizer': '120.f1.a1', 'counter': 21, 'group_counter': 5848, 'group_order': 1440, 'label': '12A', 'order': 12, 'powers': [14, 10, 21], 'representative': 15253, 'size': 120}
  • id: 108767644
    {'aut_label': '15A1', 'centralizer': '96.a1.a1', 'counter': 22, 'group_counter': 5848, 'group_order': 1440, 'label': '15A1', 'order': 15, 'powers': [23, 12, 7], 'representative': 97335, 'size': 96}
  • id: 108767645
    {'aut_label': '15A1', 'centralizer': '96.a1.a1', 'counter': 23, 'group_counter': 5848, 'group_order': 1440, 'label': '15A2', 'order': 15, 'powers': [22, 13, 7], 'representative': 121100, 'size': 96}
  • id: 108767646
    {'aut_label': '20A1', 'centralizer': '72.e1.a1', 'counter': 24, 'group_counter': 5848, 'group_order': 1440, 'label': '20A1', 'order': 20, 'powers': [17, 25, 10], 'representative': 96498, 'size': 72}
  • id: 108767647
    {'aut_label': '20A1', 'centralizer': '72.e1.a1', 'counter': 25, 'group_counter': 5848, 'group_order': 1440, 'label': '20A3', 'order': 20, 'powers': [18, 24, 10], 'representative': 162729, 'size': 72}
• 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: 4001222
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4001233
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4001235
    {'cdim': 2, 'counter': 3, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, -1, 2, -1, 0, 0, 2, 2, 2, 0, -1, 2, 2, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4001236
    {'cdim': 3, 'counter': 4, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 1, 3, -1, 1, 0, 3, 0, -1, -1, 3, 3, -1, 1, 0, -1, -1, 1, 1, -1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4001237
    {'cdim': 3, 'counter': 5, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, -1, 3, -1, -1, 0, 3, 0, 1, 1, 3, 3, -1, -1, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4001240
    {'cdim': 4, 'counter': 8, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 4, 1, 1, 4, 0, -1, -1, 1, 1, 0, -1, -1, -1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4001241
    {'cdim': 4, 'counter': 9, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.4b', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 4, 1, 1, -4, 0, -1, -1, 1, -1, 0, -1, -1, 1, 1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4001223
    {'cdim': 5, 'counter': 10, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, 1, 1, 1, 5, -1, -1, 5, 1, 0, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4001224
    {'cdim': 5, 'counter': 11, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.5b', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, 5, -5, 1, 1, -1, 5, -1, -1, -5, -1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4001238
    {'cdim': 3, 'counter': 6, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.3c', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, -2, -2, -2, 6, 0, 0, 6, -2, 1, 1, 0, 0, -2, 1, 1, 1, 1, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4001239
    {'cdim': 3, 'counter': 7, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.3d', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, 6, -6, -2, -2, 2, 6, 0, 0, -6, 2, 1, 1, 0, 0, -2, 1, 1, -1, -1, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4001226
    {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.8a', 'multiplicity': 1, 'nt': [15, 23], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, -4, 2, -1, 0, 0, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4001229
    {'cdim': 10, 'counter': 16, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.10a', 'multiplicity': 1, 'nt': [18, 145], 'qdim': 10, 'qvalues': [10, 10, 0, 2, 2, 0, -5, -2, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4001225
    {'cdim': 6, 'counter': 12, 'faithful': False, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.6a', 'multiplicity': 2, 'nt': [36, 551], 'qdim': 12, 'qvalues': [12, 12, 0, -4, -4, 0, -6, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4001230
    {'cdim': 12, 'counter': 17, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.12a', 'multiplicity': 1, 'nt': [20, 203], 'qdim': 12, 'qvalues': [12, -4, 4, 0, 0, 0, 0, 3, 0, -4, 0, -3, -3, -1, 1, 0, 1, 1, -1, -1, -1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4001231
    {'cdim': 12, 'counter': 18, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.12b', 'multiplicity': 1, 'nt': [30, 258], 'qdim': 12, 'qvalues': [12, -4, -4, 0, 0, 0, 0, 3, 0, 4, 0, -3, -3, -1, -1, 0, 1, 1, 1, 1, 1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4001232
    {'cdim': 15, 'counter': 19, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.15a', 'multiplicity': 1, 'nt': [24, 2963], 'qdim': 15, 'qvalues': [15, -5, 5, 3, -1, 1, 0, -3, 0, -5, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4001234
    {'cdim': 15, 'counter': 20, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.15b', 'multiplicity': 1, 'nt': [36, 2334], 'qdim': 15, 'qvalues': [15, -5, -5, 3, -1, -1, 0, -3, 0, 5, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4001227
    {'cdim': 9, 'counter': 14, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.9a', 'multiplicity': 2, 'nt': [36, 2335], 'qdim': 18, 'qvalues': [18, -6, -6, -6, 2, 2, 0, 0, 0, 6, -2, 3, 3, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4001228
    {'cdim': 9, 'counter': 15, 'faithful': True, 'group': '1440.5848', 'group_order': 1440, 'image': None, 'label': '1440.5848.9b', 'multiplicity': 2, 'nt': [36, 2336], 'qdim': 18, 'qvalues': [18, -6, 6, -6, 2, -2, 0, 0, 0, -6, 2, 3, 3, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, -1, -1], '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: 5675327
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1440, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1440, 'label': '1440.5848.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5675338
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1440, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 720, 'label': '1440.5848.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5675345
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 240, 'counter': 3, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 240, 'label': '1440.5848.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675346
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 60, 'counter': 4, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 60, 'label': '1440.5848.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5675347
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 60, 'counter': 5, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 60, 'label': '1440.5848.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5675348
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 6, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 24, 'label': '1440.5848.3c1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 5675349
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 7, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 24, 'label': '1440.5848.3c2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 5675350
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 8, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 12, 'label': '1440.5848.3d1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 5675351
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 9, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 12, 'label': '1440.5848.3d2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 5675328
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 10, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 24, 'label': '1440.5848.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5675329
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 11, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 12, 'label': '1440.5848.4b', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5675330
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 12, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 24, 'label': '1440.5848.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675331
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 24, 'counter': 13, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 12, 'label': '1440.5848.5b', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675332
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 4, 'counter': 14, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 4, 'label': '1440.5848.6a1', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 5675333
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 4, 'counter': 15, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 4, 'label': '1440.5848.6a2', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 5675334
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 4, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 4, 'label': '1440.5848.8a', 'nt': [15, 23], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675335
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 5, 'dim': 9, 'faithful': True, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.9a1', 'nt': [36, 2335], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 5675336
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 5, 'dim': 9, 'faithful': True, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.9a2', 'nt': [36, 2335], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 5675337
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 5, 'dim': 9, 'faithful': True, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.9b1', 'nt': [36, 2336], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 5675339
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 5, 'dim': 9, 'faithful': True, 'field': [-1, -1, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.9b2', 'nt': [36, 2336], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 5675340
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 4, 'label': '1440.5848.10a', 'nt': [18, 145], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-5, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675341
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.12a', 'nt': [20, 203], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5675342
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.12b', 'nt': [30, 258], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5675343
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 1, 'dim': 15, 'faithful': True, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.15a', 'nt': [24, 2963], 'q_character': None, 'values': [[[15, 0]], [[-5, 0]], [[5, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5675344
    {'center': '1440.a1.a1', 'center_index': 1440, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 15, 'faithful': True, 'field': [0, 1], 'group': '1440.5848', 'group_counter': 5848, 'group_order': 1440, 'image': None, 'image_isoclass': '1440.5848', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1.a1', 'kernel_order': 1, 'label': '1440.5848.15b', 'nt': [36, 2334], 'q_character': None, 'values': [[[15, 0]], [[-5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 61899002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '1440.5848.1.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': '1440.5848', 'subgroup_hash': 5848, 'subgroup_order': 1440, 'subgroup_tex': 'S_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5848.2.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', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.768', 'subgroup_hash': 768, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.3.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': '480.956', 'subgroup_hash': 956, 'subgroup_order': 480, 'subgroup_tex': 'D_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, '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: 61899101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 24, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1440.5848.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1024', 'subgroup_hash': 1024, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 240, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5848.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': False, 'special_labels': ['S', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.92', 'subgroup_hash': 92, 'subgroup_order': 240, 'subgroup_tex': 'C_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 24, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.6.d1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 61899014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 24, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.10.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 61899036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': 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: 61899047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 24, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.37', 'subgroup_hash': 37, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.38', 'subgroup_hash': 38, 'subgroup_order': 120, 'subgroup_tex': 'C_5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 61899066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.15.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 61899070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': True, 'centralizer_order': 24, 'characteristic': True, 'core_order': 60, 'counter': 25, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1440.5848.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': True, 'solvable': False, 'special_labels': ['PC', 'D3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 61899075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 12, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 61899077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.30.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 61899089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 61899091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 12, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 61899096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1440.5848.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 61899098
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899099
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 61899100
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 61899102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': True, 'centralizer_order': 60, 'characteristic': True, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1440.5848.60.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61899108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 61899122
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61899127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61899132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.90.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61899138
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 61899139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5848.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899140
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899144
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61899146
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899147
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899153
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.120.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61899005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 61899006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 61899007
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 61899008
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 61899009
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 61899010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1440.5848.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 61899011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899018
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899027
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.180.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61899028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899029
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899030
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61899032
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899033
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899034
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899035
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899037
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1440.5848.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 61899039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5848.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '360.121', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 121, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 360, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61899040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899042
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899043
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899044
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61899046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 61899051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 61899052
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 61899053
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1440.5848.360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 61899054
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899055
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899056
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 61899057
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 61899059
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 61899060
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 61899061
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 61899062
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1440.5848.720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, '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: 61899063
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1440.5848', 'ambient_counter': 5848, 'ambient_order': 1440, 'ambient_tex': 'S_4\\times A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': True, 'core_order': 1, 'counter': 154, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1440.5848.1440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1440.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1440.5848', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5848, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1440, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'C4'], '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: 61899098
    {'ambient': '1440.5848', 'aut_centralizer_order': 5, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '24.c1.a1'], 'contains': ['96.a1.a1', '144.b1.a1', '240.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7481, -1, 8080, -1, 6086, -1, 6117, -1], 'generators': [20, 1, 136934], 'label': '1440.5848.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '48.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899002
    {'ambient': '1440.5848', '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': '1440.a1.a1', 'complements': ['1440.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '4.a1.a1', '5.a1.a1', '6.d1.a1', '10.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6143, 3302, 5672, 3302, 7441, 3714, 7373, 3714], 'generators': [41062, 20, 23, 1, 87251, 16], 'label': '1440.5848.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1440.5848', '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': '1440.5848'}
  • id: 61899003
    {'ambient': '1440.5848', 'aut_centralizer_order': 3, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.189', 'aut_weyl_index': 12, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['24.a1.a1', '40.c1.a1', '48.b1.a1', '80.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8790, -1, 9015, -1, 9599, -1, 9531, -1], 'generators': [87251, 41040, 11], 'label': '1440.5848.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 61899004
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.h1.a1'], 'contains': ['360.n1.a1', '480.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7044, -1, 7121, -1, 7599, -1, 7630, -1], 'generators': [15859, 40463, 137527], 'label': '1440.5848.120.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.q1.a1', 'old_label': '120.q1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61899005
    {'ambient': '1440.5848', 'aut_centralizer_order': 40, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1'], 'contains': ['288.a1.a1', '720.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3267, -1, 4406, -1, 1190, -1, 1073, -1], 'generators': [136920, 16], 'label': '1440.5848.144.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899006
    {'ambient': '1440.5848', 'aut_centralizer_order': 20, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.a1.a1', '72.h1.a1', '72.i1.a1'], 'contains': ['288.a1.a1', '720.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6645, -1, 7237, -1, 5033, -1, 4967, -1], 'generators': [136934, 14], 'label': '1440.5848.144.b1.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': '144.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899007
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '48.b1.a1', '72.b1.a1', '72.h1.a1'], 'contains': ['288.a1.a1', '720.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8047, -1, 9078, -1, 5684, -1, 5618, -1], 'generators': [136920, 5160], 'label': '1440.5848.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899008
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.i1.a1'], 'contains': ['288.a1.a1', '720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4953, -1, 6054, -1, 2668, -1, 2403, -1], 'generators': [136920, 5183], 'label': '1440.5848.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899009
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.d1.a1', '72.h1.a1', '72.i1.a1'], 'contains': ['288.a1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6510, -1, 7506, -1, 5198, -1, 5132, -1], 'generators': [136920, 5162], 'label': '1440.5848.144.e1.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': '144.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899010
    {'ambient': '1440.5848', 'aut_centralizer_order': 18, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.c1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9199, -1, 8232, -1, 8696, -1, 8927, -1], 'generators': [15859, 11], 'label': '1440.5848.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '160.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899011
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.b1.a1', '90.a1.a1', '90.b1.a1', '90.e1.a1'], 'contains': ['360.b1.a1', '360.c1.a1', '360.e1.a1', '360.h1.a1', '360.i1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5219, -1, 5179, -1, 3916, -1, 3947, -1], 'generators': [1, 40447, 7], 'label': '1440.5848.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '1440.5848', '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': '2.1'}
  • id: 61899012
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.c1.a1', '90.a1.a1', '90.e1.a1'], 'contains': ['360.b1.a1', '360.d1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2106, -1, 1664, -1, 2157, -1, 2040, -1], 'generators': [1, 40463, 7], 'label': '1440.5848.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899013
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1', '90.c1.a1', '90.f1.a1'], 'contains': ['360.c1.a1', '360.e1.a1', '360.k1.a1', '360.m1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4565, -1, 5465, -1, 4254, -1, 4285, -1], 'generators': [40447, 137526, 7], 'label': '1440.5848.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899014
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.c1.a1', '30.d1.a1', '40.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6455, -1, 5365, -1, 7529, -1, 7461, -1], 'generators': [20, 23, 1, 16698, 162121, 16], 'label': '1440.5848.10.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 61899015
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.d1.a1', '90.c1.a1', '90.d1.a1', '90.e1.a1'], 'contains': ['360.c1.a1', '360.f1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [236, -1, 531, -1, 1943, -1, 1825, -1], 'generators': [40447, 17, 7], 'label': '1440.5848.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899016
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '90.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.d1.a1', '90.f1.a1'], 'contains': ['360.c1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2341, -1, 2673, -1, 2817, -1, 2700, -1], 'generators': [40447, 137542, 7], 'label': '1440.5848.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899017
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '90.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.a1', '90.g1.a1'], 'contains': ['360.c1.a1', '360.d1.a1', '360.j1.a1', '360.n1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4187, -1, 5015, -1, 4085, -1, 4116, -1], 'generators': [40463, 137527, 16], 'label': '1440.5848.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899018
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '90.b1.a1', '90.d1.a1', '90.g1.a1'], 'contains': ['360.c1.a1', '360.j1.a1', '360.l1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5360, -1, 5979, -1, 5429, -1, 5460, -1], 'generators': [137536, 40440, 16], 'label': '1440.5848.180.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61899019
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.f1.a1', '90.c1.a1', '90.e1.a1'], 'contains': ['360.d1.a1', '360.e1.a1', '360.f1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1492, -1, 1348, -1, 2306, -1, 2188, -1], 'generators': [40463, 17, 7], 'label': '1440.5848.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899020
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.a1', '90.f1.a1'], 'contains': ['360.d1.a1', '360.e1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2806, -1, 2422, -1, 2454, -1, 2485, -1], 'generators': [40463, 137542, 7], 'label': '1440.5848.180.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899021
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.a1', '90.f1.a1'], 'contains': ['360.d1.a1', '360.e1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2806, -1, 2267, -1, 2454, -1, 2337, -1], 'generators': [40463, 137526, 7], 'label': '1440.5848.180.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.i1.a2', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899022
    {'ambient': '1440.5848', 'aut_centralizer_order': 240, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '60.a1.a1', '60.g1.a1', '90.e1.a1'], 'contains': ['360.a1.a1', '360.b1.a1', '360.f1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [409, -1, 894, -1, 2603, -1, 2914, -1], 'generators': [23, 1, 16], 'label': '1440.5848.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '180.j1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899023
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.h1.a1', '60.i1.a1', '90.e1.a1', '90.f1.a1', '90.g1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '360.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3150, -1, 3475, -1, 3561, -1, 3592, -1], 'generators': [23, 40463, 16], 'label': '1440.5848.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.k1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899024
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '90.e1.a1', '90.f1.a1'], 'contains': ['360.a1.a1', '360.e1.a1', '360.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1710, -1, 708, -1, 3402, -1, 3244, -1], 'generators': [23, 40442, 16], 'label': '1440.5848.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.l1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899025
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '576.8653', 'aut_weyl_index': 5, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['30.f1.a1', '30.g1.a1', '30.h1.a1', '40.a1.a1', '40.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6206, -1, 5601, -1, 7841, -1, 7773, -1], 'generators': [15859, 20, 23, 137527, 40444, 16], 'label': '1440.5848.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1024'}
  • id: 61899026
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1'], 'contains': ['360.h1.a1', '360.i1.a1', '360.j1.a1', '360.k1.a1', '360.m1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5829, -1, 6684, -1, 5862, -1, 5893, -1], 'generators': [1, 40447, 137526], 'label': '1440.5848.180.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '180.m1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899027
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.a1', '60.n1.a1', '90.b1.a1'], 'contains': ['360.h1.a1', '360.k1.a1', '360.l1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7860, -1, 9586, -1, 7758, -1, 7867, -1], 'generators': [137526, 6, 40440], 'label': '1440.5848.180.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '180.n1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61899028
    {'ambient': '1440.5848', 'aut_centralizer_order': 48, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'contains': ['480.b1.a1', '720.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3600, -1, 3088, -1, 4734, -1, 4730, -1], 'generators': [15856, 16], 'label': '1440.5848.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899029
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.a1', '80.a1.a1', '120.b1.a1', '120.j1.a1', '120.k1.a1'], 'contains': ['480.b1.a1', '720.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6847, -1, 6005, -1, 6839, -1, 6851, -1], 'generators': [1, 15840], 'label': '1440.5848.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899030
    {'ambient': '1440.5848', 'aut_centralizer_order': 120, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '60.a1.a1', '80.a1.a1', '120.l1.a1'], 'contains': ['480.a1.a1', '720.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8117, -1, 8008, -1, 7486, -1, 7517, -1], 'generators': [20, 1], 'label': '1440.5848.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899031
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '60.h1.a1', '80.b1.a1', '120.l1.a1', '120.m1.a1', '120.n1.a1'], 'contains': ['480.a1.a1', '720.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [9498, -1, 9021, -1, 8274, -1, 8189, -1], 'generators': [40444, 3], 'label': '1440.5848.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.n1.a1', 'old_label': '240.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899032
    {'ambient': '1440.5848', 'aut_centralizer_order': 48, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '80.b1.a1', '120.c1.a1', '120.j1.a1'], 'contains': ['480.b1.a1', '720.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8300, -1, 7190, -1, 7197, -1, 7369, -1], 'generators': [16680, 162120], 'label': '1440.5848.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '240.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899033
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.d1.a1', '120.k1.a1'], 'contains': ['480.b1.a1', '720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4953, -1, 4791, -1, 6171, -1, 6105, -1], 'generators': [16703, 162120], 'label': '1440.5848.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899034
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '60.j1.a1', '80.c1.a1', '120.l1.a1', '120.m1.a1'], 'contains': ['480.a1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7129, -1, 8584, -1, 7882, -1, 7744, -1], 'generators': [3, 40442], 'label': '1440.5848.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.n1.a1', 'old_label': '240.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899035
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '120.e1.a1', '120.j1.a1', '120.k1.a1'], 'contains': ['480.b1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6307, -1, 6124, -1, 6987, -1, 7000, -1], 'generators': [16685, 162120], 'label': '1440.5848.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899036
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.34', 'aut_weyl_index': 24, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '60.e1.a1', '72.b1.a1', '120.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3773, -1, 4515, -1, 5289, -1, 5219, -1], 'generators': [87256, 41056, 16], 'label': '1440.5848.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '1440.5848', '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': '60.5'}
  • id: 61899037
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 240, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '80.c1.a1'], 'contains': ['480.c1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [8564, -1, 7310, -1, 8443, -1, 8432, -1], 'generators': [162123, 16685], 'label': '1440.5848.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.i1.a1', 'old_label': '240.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899038
    {'ambient': '1440.5848', 'aut_centralizer_order': 120, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '144.e1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6693, -1, 7632, -1, 5198, -1, 5132, -1], 'generators': [136920], 'label': '1440.5848.288.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '288.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899039
    {'ambient': '1440.5848', 'aut_centralizer_order': 480, 'aut_label': '360.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '6.a1.a1', 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.a1.a1', '120.h1.a1', '120.i1.a1', '180.j1.a1', '180.k1.a1', '180.l1.a1'], 'contains': ['720.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2262, 5896, 2154, 5896, 4085, 3048, 3938, 3048], 'generators': [23, 16], 'label': '1440.5848.360.a1.a1', 'mobius_quo': -1, 'mobius_sub': -180, 'normal_closure': '360.a1.a1', 'normal_contained_in': ['6.a1.a1', '120.a1.a1'], 'normal_contains': ['1440.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': '6.1', 'quotient_action_kernel': '60.5', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899040
    {'ambient': '1440.5848', 'aut_centralizer_order': 480, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.b1.a1', '180.a1.a1', '180.b1.a1', '180.j1.a1'], 'contains': ['720.a1.a1', '720.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5014, -1, 3943, -1, 3578, -1, 3075, -1], 'generators': [1, 7], 'label': '1440.5848.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '360.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899041
    {'ambient': '1440.5848', 'aut_centralizer_order': 64, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.c1.a1', '180.a1.a1', '180.c1.a1', '180.d1.a1', '180.e1.a1', '180.f1.a1', '180.g1.a1', '180.k1.a1'], 'contains': ['720.a1.a1', '720.c1.a1', '720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3878, -1, 5110, -1, 3916, -1, 3769, -1], 'generators': [40440, 16], 'label': '1440.5848.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899155
    {'ambient': '1440.5848', 'aut_centralizer_order': 3, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.h1.a1', '40.c1.a1'], 'contains': ['360.l1.a1', '480.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9942, -1, 9720, -1, 9863, -1, 9892, -1], 'generators': [15859, 137520, 40440], 'label': '1440.5848.120.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '120.p1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61899042
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.d1.a1', '180.b1.a1', '180.f1.a1', '180.h1.a1', '180.i1.a1', '180.i1.a2', '180.k1.a1'], 'contains': ['720.a1.a1', '720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3150, -1, 2630, -1, 3409, -1, 2840, -1], 'generators': [40463, 16], 'label': '1440.5848.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899043
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.e1.a1', '180.a1.a1', '180.c1.a1', '180.h1.a1', '180.i1.a1', '180.i1.a2', '180.l1.a1'], 'contains': ['720.a1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4193, -1, 4308, -1, 3747, -1, 3244, -1], 'generators': [23, 40442], 'label': '1440.5848.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899044
    {'ambient': '1440.5848', 'aut_centralizer_order': 480, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.f1.a1', '180.d1.a1', '180.h1.a1', '180.j1.a1'], 'contains': ['720.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [59, -1, 779, -1, 2413, -1, 2188, -1], 'generators': [17, 7], 'label': '1440.5848.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '360.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899045
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.g1.a1', '180.b1.a1', '180.d1.a1', '180.e1.a1', '180.i1.a1', '180.i1.a2', '180.l1.a1'], 'contains': ['720.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1742, -1, 1579, -1, 2817, -1, 2551, -1], 'generators': [23, 40453], 'label': '1440.5848.360.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899046
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.j1.a1', '120.l1.a1', '180.a1.a1', '180.m1.a1', '180.n1.a1'], 'contains': ['720.b1.a1', '720.c1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7444, -1, 7388, -1, 6511, -1, 6264, -1], 'generators': [1, 40440], 'label': '1440.5848.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '360.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899047
    {'ambient': '1440.5848', 'aut_centralizer_order': 5, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.b1.a1', '36.e1.a1', '48.a1.a1', '60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4719, -1, 6159, -1, 5891, -1, 5820, -1], 'generators': [20, 23, 1, 136934, 16], 'label': '1440.5848.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 61899048
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.k1.a1', '180.a1.a1', '180.m1.a1'], 'contains': ['720.b1.a1', '720.d1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5739, -1, 6285, -1, 5357, -1, 5291, -1], 'generators': [1, 40447], 'label': '1440.5848.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '360.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899049
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.a1', '180.g1.a1', '180.m1.a1'], 'contains': ['720.c1.a1', '720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5486, -1, 6684, -1, 5526, -1, 5460, -1], 'generators': [40447, 137527], 'label': '1440.5848.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.j1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899050
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.m1.a1', '180.c1.a1', '180.m1.a1', '180.n1.a1'], 'contains': ['720.c1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6502, -1, 8921, -1, 6680, -1, 6614, -1], 'generators': [137526, 40440], 'label': '1440.5848.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '360.k1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899051
    {'ambient': '1440.5848', 'aut_centralizer_order': 96, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.n1.a1', '120.o1.a1', '120.p1.a1', '180.g1.a1', '180.n1.a1'], 'contains': ['720.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8802, -1, 9599, -1, 8072, -1, 8643, -1], 'generators': [137520, 40440], 'label': '1440.5848.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '360.l1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61899052
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '180.m1.a1'], 'contains': ['720.d1.a1', '720.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5350, -1, 6484, -1, 6012, -1, 5946, -1], 'generators': [40447, 137526], 'label': '1440.5848.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '360.m1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899053
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.q1.a1', '180.f1.a1'], 'contains': ['720.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5214, -1, 5610, -1, 5843, -1, 5777, -1], 'generators': [40463, 137527], 'label': '1440.5848.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.a1', 'old_label': '360.n1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61899054
    {'ambient': '1440.5848', 'aut_centralizer_order': 360, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '120.a1.a1', '160.a1.a1', '240.c1.a1', '240.d1.a1', '240.g1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8441, -1, 8445, -1, 7486, -1, 7517, -1], 'generators': [20], 'label': '1440.5848.480.a1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899055
    {'ambient': '1440.5848', 'aut_centralizer_order': 144, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.o1.a1', '160.a1.a1', '240.a1.a1', '240.b1.a1', '240.e1.a1', '240.f1.a1', '240.h1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6784, -1, 6026, -1, 6913, -1, 6925, -1], 'generators': [15840], 'label': '1440.5848.480.b1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '480.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899056
    {'ambient': '1440.5848', 'aut_centralizer_order': 18, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.a1', '120.p1.a1', '120.q1.a1', '160.a1.a1', '240.i1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [8624, -1, 7774, -1, 8094, -1, 7997, -1], 'generators': [15859], 'label': '1440.5848.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.c1.a1', 'old_label': '480.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61899057
    {'ambient': '1440.5848', 'aut_centralizer_order': 960, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.a1', '360.a1.a1', '360.b1.a1', '360.c1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '360.g1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3360, -1, 3407, -1, 3662, -1, 3159, -1], 'generators': [16], 'label': '1440.5848.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899058
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '36.f1.a1', '48.b1.a1', '60.h1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5007, -1, 6803, -1, 6437, -1, 6367, -1], 'generators': [20, 23, 5164, 136940, 16], 'label': '1440.5848.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '240.194'}
  • id: 61899059
    {'ambient': '1440.5848', 'aut_centralizer_order': 480, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '240.b1.a1', '240.c1.a1', '360.b1.a1', '360.h1.a1', '360.i1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6876, -1, 6783, -1, 6363, -1, 6115, -1], 'generators': [1], 'label': '1440.5848.720.b1.a1', 'mobius_quo': None, 'mobius_sub': -120, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899060
    {'ambient': '1440.5848', 'aut_centralizer_order': 192, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.d1.a1', '240.e1.a1', '360.c1.a1', '360.h1.a1', '360.j1.a1', '360.k1.a1', '360.l1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7917, -1, 7605, -1, 6659, -1, 6412, -1], 'generators': [40440], 'label': '1440.5848.720.c1.a1', 'mobius_quo': None, 'mobius_sub': -48, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899061
    {'ambient': '1440.5848', 'aut_centralizer_order': 64, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.c1.a1', '360.d1.a1', '360.i1.a1', '360.j1.a1', '360.m1.a1', '360.n1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5214, -1, 5610, -1, 5526, -1, 5460, -1], 'generators': [40463], 'label': '1440.5848.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899062
    {'ambient': '1440.5848', 'aut_centralizer_order': 32, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.g1.a1', '240.h1.a1', '240.i1.a1', '360.e1.a1', '360.h1.a1', '360.i1.a1', '360.k1.a1', '360.m1.a1'], 'contains': ['1440.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6247, -1, 7135, -1, 6511, -1, 6264, -1], 'generators': [40442], 'label': '1440.5848.720.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1.a1', 'old_label': '720.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899063
    {'ambient': '1440.5848', 'aut_centralizer_order': None, 'aut_label': '1440.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': ['288.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1', '720.a1.a1', '720.b1.a1', '720.c1.a1', '720.d1.a1', '720.e1.a1'], 'contains': [], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6784, 7311, 7135, 7311, 6511, 4857, 6264, 4857], 'generators': [], 'label': '1440.5848.1440.a1.a1', 'mobius_quo': 1, 'mobius_sub': 720, 'normal_closure': '1440.a1.a1', 'normal_contained_in': ['24.a1.a1', '360.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1440.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61899064
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.b1.a1', '36.g1.a1', '48.c1.a1', '60.j1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4530, -1, 6421, -1, 6123, -1, 6053, -1], 'generators': [20, 23, 5162, 136940, 16], 'label': '1440.5848.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '240.194'}
  • id: 61899065
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.34', 'aut_weyl_index': 24, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '60.m1.a1', '72.h1.a1', '120.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7726, -1, 7900, -1, 8729, -1, 8661, -1], 'generators': [1, 87240, 41041], 'label': '1440.5848.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 61899066
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '96.226', 'aut_weyl_index': 30, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.g1.a1', '45.a1.a1', '60.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3421, -1, 3577, -1, 4524, -1, 4474, -1], 'generators': [23, 1, 15856, 40463, 137526, 16], 'label': '1440.5848.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61899067
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '15.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.d1.a1', '30.e1.a1', '30.f1.a1', '45.a1.a1', '60.n1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5432, -1, 6645, -1, 7113, -1, 7045, -1], 'generators': [20, 23, 1, 137526, 40444, 16], 'label': '1440.5848.15.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '15.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 61899068
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.dv', 'aut_weyl_index': 1, 'centralizer': '1440.a1.a1', 'complements': ['720.e1.a1', '720.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '8.a1.a1', '10.b1.a1', '12.c1.a1', '20.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6079, 5330, 5729, 5330, 7711, 6191, 7643, 6191], 'generators': [20, 23, 87251, 41056, 16], 'label': '1440.5848.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1440.5848', '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': '1440.5848'}
  • id: 61899069
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '6.d1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '90.e1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1968, -1, 2544, -1, 1054, -1, 1145, -1], 'generators': [23, 136934, 16, 14, 5183], 'label': '1440.5848.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 61899070
    {'ambient': '1440.5848', 'aut_centralizer_order': 6, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.a1.a1', '60.g1.a1', '80.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6092, -1, 5320, -1, 7352, -1, 7284, -1], 'generators': [15859, 20, 23, 1, 16], 'label': '1440.5848.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 61899071
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.h1.a1', '60.i1.a1', '80.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6318, -1, 5743, -1, 8140, -1, 8072, -1], 'generators': [20, 23, 16, 16692, 162120], 'label': '1440.5848.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 61899072
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['40.a1.a1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '80.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6505, -1, 5105, -1, 7585, -1, 7517, -1], 'generators': [20, 23, 16698, 16, 162120], 'label': '1440.5848.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 61899073
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '5.a1.a1'], 'contains': ['40.c1.a1', '60.m1.a1', '60.n1.a1', '80.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '20T203', 'count': 20, 'diagramx': [8413, -1, 8891, -1, 9242, -1, 9018, -1], 'generators': [15859, 40459, 137526, 6, 11], 'label': '1440.5848.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '20.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 61899074
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.34', 'aut_weyl_index': 24, 'centralizer': '60.a1.a1', 'complements': ['60.a1.a1', '60.j1.a1', '60.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.e1.a1'], 'contains': ['120.o1.a1', '144.c1.a1', '240.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8847, 8726, 8208, 8726, 8424, 6714, 8704, 6714], 'generators': [87240, 41040], 'label': '1440.5848.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['1440.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 61899075
    {'ambient': '1440.5848', 'aut_centralizer_order': 5, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['72.g1.a1', '96.a1.a1', '120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4700, -1, 6437, -1, 6218, -1, 6218, -1], 'generators': [20, 23, 136940, 16], 'label': '1440.5848.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 61899076
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.h1.a1', '120.l1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '24T2963', 'count': 24, 'diagramx': [7592, -1, 8559, -1, 6655, -1, 6804, -1], 'generators': [1, 5164, 136925, 3], 'label': '1440.5848.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '24.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 61899077
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '60.m1.a1', '90.b1.a1', '120.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '30T262', 'count': 15, 'diagramx': [6581, -1, 7144, -1, 5590, -1, 5520, -1], 'generators': [1, 40447, 137526, 15840, 7], 'label': '1440.5848.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61899078
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '90.d1.a1', '120.f1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '30T258', 'count': 15, 'diagramx': [1354, -1, 2709, -1, 3829, -1, 3846, -1], 'generators': [40447, 17, 15840, 137542, 7], 'label': '1440.5848.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61899079
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1186', 'aut_weyl_index': 6, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '15.a1.a1', '18.a1.a1', '30.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3275, -1, 3554, -1, 4524, -1, 4474, -1], 'generators': [41062, 23, 1, 87247, 16], 'label': '1440.5848.3.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': '1440.5848', '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': '240.190'}
  • id: 61899080
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '10.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '60.f1.a1', '60.g1.a1', '60.i1.a1', '60.k1.a1', '90.e1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1647, -1, 1243, -1, 4285, -1, 4180, -1], 'generators': [162134, 23, 16698, 16, 14], 'label': '1440.5848.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '30.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61899081
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.a1.a1', '15.b1.a1'], 'contains': ['60.a1.a1', '60.h1.a1', '60.j1.a1', '90.e1.a1', '120.l1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5342, -1, 5975, -1, 6796, -1, 6647, -1], 'generators': [20, 23, 1, 40444, 16], 'label': '1440.5848.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899082
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1'], 'contains': ['60.h1.a1', '60.j1.a1', '90.f1.a1', '120.m1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5052, -1, 6327, -1, 7074, -1, 7006, -1], 'generators': [20, 23, 137526, 40444, 16], 'label': '1440.5848.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899083
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '15.b1.a1'], 'contains': ['60.h1.a1', '90.g1.a1', '120.n1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5584, -1, 6822, -1, 7841, -1, 7773, -1], 'generators': [20, 23, 137527, 40444, 16], 'label': '1440.5848.30.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 61899084
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '90.g1.a1', '120.h1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4070, -1, 3992, -1, 4909, -1, 4918, -1], 'generators': [23, 15856, 40463, 137527, 16], 'label': '1440.5848.30.g1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 61899085
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '288.1026', 'aut_weyl_index': 10, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['90.g1.a1', '120.i1.a1', '120.p1.a1', '120.q1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6869, -1, 5703, -1, 8473, -1, 8405, -1], 'generators': [15859, 23, 40463, 137527, 16], 'label': '1440.5848.30.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '30.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 61899086
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '18.a1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '72.h1.a1', '72.i1.a1', '180.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '36T2333', 'count': 18, 'diagramx': [4586, -1, 4672, -1, 1601, -1, 1601, -1], 'generators': [136934, 5160, 16, 14], 'label': '1440.5848.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '1440.5848', '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': '20.4'}
  • id: 61899087
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.f1.a1', '180.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '36T2336', 'count': 18, 'diagramx': [2211, -1, 2986, -1, 360, -1, 360, -1], 'generators': [136934, 16, 14, 5183], 'label': '1440.5848.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 61899088
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '72.f1.a1', '180.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '36T2334', 'count': 18, 'diagramx': [705, -1, 1739, -1, 123, -1, 123, -1], 'generators': [136929, 5160, 9, 16], 'label': '1440.5848.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 61899089
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.e1.a1', '180.h1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '36T2335', 'count': 18, 'diagramx': [1210, -1, 2753, -1, 547, -1, 547, -1], 'generators': [136929, 9, 16, 5183], 'label': '1440.5848.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 61899090
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.767', 'aut_weyl_index': 4, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.e1.a1', '20.d1.a1', '24.c1.a1', '40.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8462, -1, 8645, -1, 8814, -1, 8834, -1], 'generators': [20, 1, 87260, 41041], 'label': '1440.5848.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 61899091
    {'ambient': '1440.5848', 'aut_centralizer_order': 10, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.g1.a1', '180.j1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1011, -1, 2062, -1, 780, -1, 780, -1], 'generators': [23, 136934, 16, 14], 'label': '1440.5848.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61899092
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '12.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.g1.a1', '180.k1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3467, -1, 3921, -1, 1275, -1, 1275, -1], 'generators': [23, 136920, 16, 5183], 'label': '1440.5848.36.f1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 61899093
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.g1.a1', '180.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1921, -1, 2370, -1, 1017, -1, 1017, -1], 'generators': [23, 136920, 5162, 16], 'label': '1440.5848.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 61899094
    {'ambient': '1440.5848', 'aut_centralizer_order': 6, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['120.a1.a1', '120.h1.a1', '120.i1.a1', '160.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6219, -1, 5406, -1, 7975, -1, 7975, -1], 'generators': [15859, 20, 23, 16], 'label': '1440.5848.40.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 61899095
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.c1.a1', '120.j1.a1', '120.l1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '40T1206', 'count': 40, 'diagramx': [8539, -1, 7431, -1, 9263, -1, 9420, -1], 'generators': [1, 16685, 3, 162121], 'label': '1440.5848.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 61899096
    {'ambient': '1440.5848', 'aut_centralizer_order': 3, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '10.b1.a1', '20.d1.a1'], 'contains': ['120.n1.a1', '120.o1.a1', '120.p1.a1', '160.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': '40T1200', 'count': 20, 'diagramx': [9441, -1, 9217, -1, 9879, -1, 9879, -1], 'generators': [15859, 40459, 137520, 11], 'label': '1440.5848.40.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61899097
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.b1.a1'], 'contains': ['90.a1.a1', '90.b1.a1', '90.c1.a1', '90.d1.a1', '90.e1.a1', '90.f1.a1', '90.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2671, -1, 3096, -1, 3514, -1, 3155, -1], 'generators': [23, 1, 40463, 137526, 16], 'label': '1440.5848.45.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61899099
    {'ambient': '1440.5848', 'aut_centralizer_order': 3, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '24.c1.a1'], 'contains': ['96.a1.a1', '144.c1.a1', '240.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8134, -1, 9305, -1, 7008, -1, 7039, -1], 'generators': [136923, 5164, 3], 'label': '1440.5848.48.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '48.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 61899100
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '24.c1.a1'], 'contains': ['96.a1.a1', '144.e1.a1', '240.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6762, -1, 8737, -1, 6398, -1, 6428, -1], 'generators': [136923, 5162, 3], 'label': '1440.5848.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '48.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 61899101
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '576.8653', 'aut_weyl_index': 5, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.a1', '15.a1.a1', '15.b1.a1', '20.a1.a1', '20.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6349, -1, 5555, -1, 7352, -1, 7284, -1], 'generators': [15859, 20, 23, 1, 137526, 40444, 16], 'label': '1440.5848.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1024'}
  • id: 61899102
    {'ambient': '1440.5848', 'aut_centralizer_order': 120, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '24.a1.a1', 'complements': ['24.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.a1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '180.j1.a1', '240.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5689, 1274, 5695, 1274, 6948, 1286, 6511, 1286], 'generators': [20, 23, 1, 16], 'label': '1440.5848.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.5', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899103
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '30.c1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.e1.a1', '120.j1.a1', '120.k1.a1', '180.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4847, -1, 4785, -1, 5233, -1, 5233, -1], 'generators': [162134, 16685, 16, 14], 'label': '1440.5848.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899104
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1'], 'contains': ['120.b1.a1', '120.d1.a1', '120.g1.a1', '180.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3105, -1, 2373, -1, 3751, -1, 3751, -1], 'generators': [162134, 16698, 16, 14], 'label': '1440.5848.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61899105
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '30.c1.a1'], 'contains': ['120.c1.a1', '120.f1.a1', '120.g1.a1', '180.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [277, -1, 97, -1, 3233, -1, 3516, -1], 'generators': [162129, 16698, 9, 16], 'label': '1440.5848.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899106
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '30.a1.a1', '30.b1.a1', '30.g1.a1'], 'contains': ['120.o1.a1', '180.g1.a1', '240.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5861, -1, 6642, -1, 5860, -1, 5860, -1], 'generators': [137536, 15856, 40440, 16], 'label': '1440.5848.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61899107
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1'], 'contains': ['120.d1.a1', '120.e1.a1', '120.f1.a1', '180.h1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1617, -1, 1424, -1, 3938, -1, 3938, -1], 'generators': [162129, 16685, 9, 16], 'label': '1440.5848.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61899108
    {'ambient': '1440.5848', 'aut_centralizer_order': 12, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '20.a1.a1', '30.c1.a1'], 'contains': ['120.b1.a1', '120.f1.a1', '120.h1.a1', '180.j1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1238, -1, 1172, -1, 4171, -1, 4171, -1], 'generators': [23, 1, 15856, 16], 'label': '1440.5848.60.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61899109
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.b1.a1', '30.d1.a1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.a1.a1', '180.k1.a1', '240.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5448, -1, 6353, -1, 7389, -1, 7389, -1], 'generators': [20, 23, 40444, 16], 'label': '1440.5848.60.h1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899110
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '20.b1.a1', '30.c1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.h1.a1', '180.k1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3514, -1, 3388, -1, 4664, -1, 4664, -1], 'generators': [23, 16703, 16, 162120], 'label': '1440.5848.60.i1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '60.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 61899111
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.c1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.a1.a1', '180.l1.a1', '240.g1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5225, -1, 5975, -1, 7096, -1, 7096, -1], 'generators': [20, 23, 40442, 16], 'label': '1440.5848.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.j1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899112
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '720.767', 'aut_weyl_index': 4, 'centralizer': '360.a1.a1', 'complements': ['240.c1.a1', '240.g1.a1', '240.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.g1.a1', '36.f1.a1', '60.i1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3836, 8443, 3896, 8443, 4850, 6714, 4810, 6714], 'generators': [23, 87247, 41056, 16], 'label': '1440.5848.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['24.a1.a1', '360.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 61899113
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '30.c1.a1'], 'contains': ['120.e1.a1', '120.g1.a1', '120.h1.a1', '180.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2336, -1, 582, -1, 4408, -1, 4408, -1], 'generators': [23, 16698, 16, 162120], 'label': '1440.5848.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.k1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61899114
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1'], 'contains': ['120.i1.a1', '180.l1.a1', '240.i1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6310, -1, 5211, -1, 7604, -1, 7682, -1], 'generators': [23, 16698, 162140, 16], 'label': '1440.5848.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.l1.a1', 'old_label': '60.l1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899115
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.d1.a1', '30.a1.a1'], 'contains': ['120.o1.a1', '180.n1.a1', '240.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7890, -1, 8378, -1, 8717, -1, 8490, -1], 'generators': [137526, 6, 15840, 40440], 'label': '1440.5848.60.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.m1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61899116
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1', '20.d1.a1'], 'contains': ['120.l1.a1', '120.m1.a1', '120.n1.a1', '180.n1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8918, -1, 9903, -1, 9018, -1, 9018, -1], 'generators': [1, 40444, 3, 137521], 'label': '1440.5848.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '60.n1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61899117
    {'ambient': '1440.5848', 'aut_centralizer_order': 20, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.e1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '360.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4328, -1, 4227, -1, 931, -1, 813, -1], 'generators': [136934, 16, 14], 'label': '1440.5848.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '1440.5848', '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': '4.2'}
  • id: 61899118
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '36.a1.a1', '36.c1.a1', '36.f1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.d1.a1', '360.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3902, -1, 4436, -1, 1710, -1, 1592, -1], 'generators': [136920, 5160, 16], 'label': '1440.5848.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899119
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.a1', '36.f1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '360.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3120, -1, 3632, -1, 671, -1, 553, -1], 'generators': [136920, 16, 5183], 'label': '1440.5848.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 61899120
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '36.g1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '360.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4054, -1, 4712, -1, 1190, -1, 1073, -1], 'generators': [23, 136920, 5162], 'label': '1440.5848.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 61899121
    {'ambient': '1440.5848', 'aut_centralizer_order': 20, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.a1', '36.e1.a1'], 'contains': ['144.a1.a1', '360.f1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [612, -1, 1718, -1, 298, -1, 180, -1], 'generators': [136929, 9, 16], 'label': '1440.5848.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899122
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '36.g1.a1'], 'contains': ['144.a1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1495, -1, 1868, -1, 483, -1, 366, -1], 'generators': [23, 5173, 136920], 'label': '1440.5848.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 61899123
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.189', 'aut_weyl_index': 12, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '30.a1.a1', '36.a1.a1', '60.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4732, -1, 4966, -1, 5229, -1, 5202, -1], 'generators': [41046, 1, 87247, 7], 'label': '1440.5848.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 61899124
    {'ambient': '1440.5848', 'aut_centralizer_order': 20, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.a1.a1', '360.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1835, -1, 2712, -1, 1450, -1, 1333, -1], 'generators': [23, 136920, 16], 'label': '1440.5848.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899125
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '24.c1.a1', '36.a1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.e1.a1', '360.h1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7080, -1, 7872, -1, 5684, -1, 5715, -1], 'generators': [136934, 5160, 14], 'label': '1440.5848.72.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899126
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.e1.a1', '360.i1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6068, -1, 6628, -1, 3738, -1, 3769, -1], 'generators': [5176, 136934, 14], 'label': '1440.5848.72.i1.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': '72.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 61899127
    {'ambient': '1440.5848', 'aut_centralizer_order': 6, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.d1.a1', '40.b1.a1'], 'contains': ['160.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8558, -1, 7431, -1, 8671, -1, 8702, -1], 'generators': [15859, 6, 11], 'label': '1440.5848.80.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899128
    {'ambient': '1440.5848', 'aut_centralizer_order': 6, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.b1.a1', '40.b1.a1'], 'contains': ['160.a1.a1', '240.d1.a1', '240.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9542, -1, 8680, -1, 9649, -1, 9677, -1], 'generators': [16692, 162120, 12], 'label': '1440.5848.80.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899129
    {'ambient': '1440.5848', 'aut_centralizer_order': 2, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '40.b1.a1'], 'contains': ['160.a1.a1', '240.g1.a1', '240.h1.a1', '240.i1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8116, -1, 7179, -1, 9055, -1, 8935, -1], 'generators': [16685, 3, 162120], 'label': '1440.5848.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 61899130
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.e1.a1', '180.f1.a1', '180.i1.a1', '180.i1.a2'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2889, -1, 2360, -1, 2549, -1, 2549, -1], 'generators': [1, 40463, 137526, 7], 'label': '1440.5848.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899131
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '90.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.c1.a1', '180.g1.a1', '180.m1.a1', '180.n1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6095, -1, 6213, -1, 5635, -1, 5635, -1], 'generators': [1, 40447, 137526, 7], 'label': '1440.5848.90.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61899132
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1'], 'contains': ['180.c1.a1', '180.d1.a1', '180.f1.a1', '180.h1.a1', '180.i1.a1', '180.i1.a2'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2403, -1, 1747, -1, 2267, -1, 2267, -1], 'generators': [40463, 137526, 17, 7], 'label': '1440.5848.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899133
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '90.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '45.a1.a1'], 'contains': ['180.d1.a1', '180.e1.a1', '180.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1526, -1, 2604, -1, 2852, -1, 2852, -1], 'generators': [40447, 17, 137542, 7], 'label': '1440.5848.90.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61899134
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.189', 'aut_weyl_index': 12, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '30.b1.a1', '36.c1.a1', '60.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [854, -1, 1585, -1, 4008, -1, 3846, -1], 'generators': [41062, 87247, 17, 7], 'label': '1440.5848.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 61899135
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.c1.a1', '30.d1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.d1.a1', '180.h1.a1', '180.j1.a1', '180.k1.a1', '180.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [932, -1, 1096, -1, 1984, -1, 1984, -1], 'generators': [23, 1, 40463, 16], 'label': '1440.5848.90.e1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899136
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '180.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '45.a1.a1'], 'contains': ['180.c1.a1', '180.e1.a1', '180.i1.a1', '180.i1.a2', '180.k1.a1', '180.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2661, -1, 2848, -1, 3514, -1, 3155, -1], 'generators': [23, 40463, 137526, 16], 'label': '1440.5848.90.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899137
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '90.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.g1.a1', '30.h1.a1', '45.a1.a1'], 'contains': ['180.f1.a1', '180.g1.a1', '180.k1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4615, -1, 5162, -1, 4909, -1, 4909, -1], 'generators': [23, 40463, 137527, 16], 'label': '1440.5848.90.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '90.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61899138
    {'ambient': '1440.5848', 'aut_centralizer_order': 15, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'contains': ['288.a1.a1', '480.a1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7625, -1, 9091, -1, 6336, -1, 6439, -1], 'generators': [20, 136940], 'label': '1440.5848.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '96.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899139
    {'ambient': '1440.5848', 'aut_centralizer_order': 120, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '24.a1.a1', 'complements': ['12.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.a1', '60.a1.a1', '60.h1.a1', '60.j1.a1'], 'contains': ['360.a1.a1', '480.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5437, 3538, 5430, 3538, 6791, 1286, 6596, 1286], 'generators': [20, 23, 16], 'label': '1440.5848.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': 60, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['2.a1.a1', '60.a1.a1'], 'normal_contains': ['360.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '1440.5848', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.5', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899140
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '60.b1.a1', '60.c1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '360.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4931, -1, 3765, -1, 4627, -1, 4658, -1], 'generators': [1, 15840, 7], 'label': '1440.5848.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.b1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899141
    {'ambient': '1440.5848', 'aut_centralizer_order': 16, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '60.b1.a1', '60.d1.a1', '60.i1.a1'], 'contains': ['240.a1.a1', '240.e1.a1', '240.f1.a1', '360.c1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4272, -1, 3937, -1, 5270, -1, 5301, -1], 'generators': [16680, 16, 162120], 'label': '1440.5848.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.c1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899142
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.f1.a1', '60.i1.a1'], 'contains': ['240.a1.a1', '240.f1.a1', '360.d1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3842, -1, 3178, -1, 4412, -1, 4443, -1], 'generators': [16703, 16, 162120], 'label': '1440.5848.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899143
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.f1.a1', '60.k1.a1'], 'contains': ['240.a1.a1', '240.h1.a1', '360.e1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4089, -1, 4687, -1, 4841, -1, 4872, -1], 'generators': [16685, 16, 162120], 'label': '1440.5848.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.e1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899144
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '60.d1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '360.f1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [58, -1, 386, -1, 3048, -1, 3079, -1], 'generators': [17, 15840, 7], 'label': '1440.5848.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.f1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61899145
    {'ambient': '1440.5848', 'aut_centralizer_order': 1, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '18.a1.a1', '24.c1.a1', '30.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4360, -1, 6429, -1, 6258, -1, 6187, -1], 'generators': [20, 23, 1, 136934, 5164, 16], 'label': '1440.5848.6.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '6.d1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '240.194'}
  • id: 61899146
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.d1.a1', '60.k1.a1'], 'contains': ['240.a1.a1', '360.g1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1439, -1, 130, -1, 3233, -1, 3413, -1], 'generators': [16698, 16, 162120], 'label': '1440.5848.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.g1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899147
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '120.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '40.a1.a1', '60.g1.a1', '60.i1.a1', '60.k1.a1'], 'contains': ['240.a1.a1', '360.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1628, -1, 1958, -1, 5056, -1, 5087, -1], 'generators': [23, 15856, 16], 'label': '1440.5848.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61899148
    {'ambient': '1440.5848', 'aut_centralizer_order': 6, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.h1.a1', '40.a1.a1', '60.l1.a1'], 'contains': ['360.a1.a1', '480.c1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5724, -1, 5310, -1, 7224, -1, 7255, -1], 'generators': [15859, 23, 16], 'label': '1440.5848.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '120.i1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 61899149
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '40.b1.a1', '60.b1.a1'], 'contains': ['240.b1.a1', '240.e1.a1', '240.h1.a1', '360.h1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7662, -1, 6679, -1, 7373, -1, 7404, -1], 'generators': [162125, 16685, 5], 'label': '1440.5848.120.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.j1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899150
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1'], 'contains': ['240.b1.a1', '240.f1.a1', '240.h1.a1', '360.i1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6230, -1, 5738, -1, 6643, -1, 6822, -1], 'generators': [162134, 16685, 14], 'label': '1440.5848.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899151
    {'ambient': '1440.5848', 'aut_centralizer_order': 8, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '30.d1.a1', '40.b1.a1', '60.n1.a1'], 'contains': ['240.c1.a1', '240.d1.a1', '240.g1.a1', '360.h1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8838, -1, 8768, -1, 8152, -1, 8183, -1], 'generators': [1, 40444, 3], 'label': '1440.5848.120.l1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.n1.a1', 'old_label': '120.l1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899152
    {'ambient': '1440.5848', 'aut_centralizer_order': 4, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '360.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '60.n1.a1'], 'contains': ['240.d1.a1', '240.g1.a1', '360.k1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7479, -1, 9393, -1, 8300, -1, 8331, -1], 'generators': [40444, 3, 137521], 'label': '1440.5848.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.n1.a1', 'old_label': '120.m1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61899153
    {'ambient': '1440.5848', 'aut_centralizer_order': 12, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '120.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '40.c1.a1', '60.n1.a1'], 'contains': ['240.d1.a1', '360.l1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9769, -1, 9893, -1, 9368, -1, 9397, -1], 'generators': [40444, 3, 137520], 'label': '1440.5848.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '120.n1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61899154
    {'ambient': '1440.5848', 'aut_centralizer_order': 24, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.c1.a1', '60.e1.a1', '60.m1.a1'], 'contains': ['360.l1.a1', '480.b1.a1'], 'core': '1440.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8696, -1, 8396, -1, 8886, -1, 9183, -1], 'generators': [137520, 15840, 40440], 'label': '1440.5848.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '1440.5848', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}