Abstract group data - 1920.241004

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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': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [6, 6], 'aut_gens': [[234027620327443354224606967333172691, 261273430356867650534376951981774161], [221771076682694396348075282764217673, 146457859963491859132527588950279167], [35941977009997158838543247831403263, 192303824238160020831078040087877952]], 'aut_group': '1920.240996', 'aut_hash': 3616852219197380499, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 80, 'aut_perms': [20405484719532562395953926338449785193956765975318207773353344818981925662942593807101973398347906124701638191886764935, 62421766004678059680911381020712119089461143856523397868360601197924085487010510786622862351491077149167745396975454262], 'aut_phi_ratio': 3.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 1], [2, 120, 1, 1], [3, 80, 1, 1], [4, 20, 1, 1], [4, 120, 1, 1], [5, 192, 2, 1], [6, 80, 1, 1], [6, 160, 2, 1], [8, 240, 1, 1], [10, 192, 2, 1], [12, 160, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4: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': 120, 'autcentquo_group': '1920.240996', 'autcentquo_hash': 3616852219197380499, 'autcentquo_nilpotent': False, 'autcentquo_order': 1920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^4:S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 10, 1], [2, 120, 1], [3, 80, 1], [4, 20, 1], [4, 120, 1], [5, 192, 2], [6, 80, 1], [6, 160, 2], [8, 240, 1], [10, 192, 2], [12, 160, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '960.11358', 'commutator_count': 2, 'commutator_label': '1920.241004', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '60.5'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 241004, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 1], [2, 120, 1, 1], [3, 80, 1, 1], [4, 20, 1, 1], [4, 120, 1, 1], [5, 192, 2, 1], [6, 80, 1, 1], [6, 160, 2, 1], [8, 240, 1, 1], [10, 192, 2, 1], [12, 160, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1140, 'exponent': 120, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 1, 2], [16, 1, 1], [24, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '960.11358', 'hash': 241004, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [5, 6], 'inner_gens': [[234027620327443354224606967333172691, 230153610659843891568486519098158764], [88820510917299721815315454850973118, 261273430356867650534376951981774161]], 'inner_hash': 11358, 'inner_nilpotent': False, 'inner_order': 960, 'inner_split': True, 'inner_tex': 'C_2^4:A_5', 'inner_used': [1, 2], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 1], [3, 2], [4, 1], [5, 4], [8, 2], [10, 2], [15, 1], [16, 1], [20, 1], [24, 1]], 'label': '1920.241004', 'linC_count': 2, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 2, 'linQ_dim': 16, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2.C2^4: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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 16, 'number_divisions': 13, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 82, 'number_subgroup_classes': 86, 'number_subgroups': 3243, 'old_label': None, 'order': 1920, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 131], [3, 80], [4, 140], [5, 384], [6, 400], [8, 240], [10, 384], [12, 160]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [104883165122394567232040289773682370], 'outer_gens': [[208413219678126407499270430342936663, 190313436779034913174001503327560773]], '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': True, 'permutation_degree': 32, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [5, 2], [6, 1], [10, 3], [15, 1], [16, 2], [20, 1], [24, 1]], 'representations': {'Perm': {'d': 32, 'gens': [234027620327443354224606967333172691, 261273430356867650534376951981774161]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2.C_2^4:A_5', 'transitive_degree': 32, '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: 109132935
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 241004, 'group_order': 1920, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109132943
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 241004, 'group_order': 1920, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 43338244971230914875922057098785435, 'size': 1}
  • id: 109132944
    {'aut_label': '2B', 'centralizer': '10.a1.a1', 'counter': 3, 'group_counter': 241004, 'group_order': 1920, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 263103653332413713025184265980594871, 'size': 10}
  • id: 109132945
    {'aut_label': '2C', 'centralizer': '120.e1.a1', 'counter': 4, 'group_counter': 241004, 'group_order': 1920, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 636618440766663245378307583253422, 'size': 120}
  • id: 109132946
    {'aut_label': '3A', 'centralizer': '80.a1.a1', 'counter': 5, 'group_counter': 241004, 'group_order': 1920, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 9146666470280554752901588357440, 'size': 80}
  • id: 109132947
    {'aut_label': '4A', 'centralizer': '20.b1.a1', 'counter': 6, 'group_counter': 241004, 'group_order': 1920, 'label': '4A', 'order': 4, 'powers': [2, 6, 6], 'representative': 146659707431019062434063373472887500, 'size': 20}
  • id: 109132948
    {'aut_label': '4B', 'centralizer': '120.f1.a1', 'counter': 7, 'group_counter': 241004, 'group_order': 1920, 'label': '4B', 'order': 4, 'powers': [3, 7, 7], 'representative': 243101000711805184380696800091991819, 'size': 120}
  • id: 109132949
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 8, 'group_counter': 241004, 'group_order': 1920, 'label': '5A1', 'order': 5, 'powers': [9, 9, 1], 'representative': 82701695137953228043997865296416482, 'size': 192}
  • id: 109132950
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 9, 'group_counter': 241004, 'group_order': 1920, 'label': '5A2', 'order': 5, 'powers': [8, 8, 1], 'representative': 123774827154737859116037670114995814, 'size': 192}
  • id: 109132936
    {'aut_label': '6A', 'centralizer': '80.a1.a1', 'counter': 10, 'group_counter': 241004, 'group_order': 1920, 'label': '6A', 'order': 6, 'powers': [5, 2, 10], 'representative': 89238087523614696345438804004514372, 'size': 80}
  • id: 109132937
    {'aut_label': '6B1', 'centralizer': '160.a1.a1', 'counter': 11, 'group_counter': 241004, 'group_order': 1920, 'label': '6B1', 'order': 6, 'powers': [5, 3, 12], 'representative': 263076844856564343643758086814507311, 'size': 160}
  • id: 109132938
    {'aut_label': '6B1', 'centralizer': '160.a1.a1', 'counter': 12, 'group_counter': 241004, 'group_order': 1920, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 11], 'representative': 263111602249406106626142470564780951, 'size': 160}
  • id: 109132939
    {'aut_label': '8A', 'centralizer': '240.g1.a1', 'counter': 13, 'group_counter': 241004, 'group_order': 1920, 'label': '8A', 'order': 8, 'powers': [6, 13, 13], 'representative': 38824336701889584172577025769374980, 'size': 240}
  • id: 109132940
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 14, 'group_counter': 241004, 'group_order': 1920, 'label': '10A1', 'order': 10, 'powers': [8, 15, 2], 'representative': 240941868431073482508396388426076510, 'size': 192}
  • id: 109132941
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 15, 'group_counter': 241004, 'group_order': 1920, 'label': '10A3', 'order': 10, 'powers': [9, 14, 2], 'representative': 67947564089132888918377288297236110, 'size': 192}
  • id: 109132942
    {'aut_label': '12A', 'centralizer': '160.c1.a1', 'counter': 16, 'group_counter': 241004, 'group_order': 1920, 'label': '12A', 'order': 12, 'powers': [10, 6, 16], 'representative': 75660841895847261950114348894615064, 'size': 160}
• 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: 4154772
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4154778
    {'cdim': 4, 'counter': 3, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 1, 4, 0, -1, -1, 1, 1, 1, 0, -1, -1, 1], 'schur_index': 1}
  • id: 4154779
    {'cdim': 5, 'counter': 4, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, 1, -1, 5, 1, 0, 0, -1, -1, -1, 1, 0, 0, -1], 'schur_index': 1}
  • id: 4154780
    {'cdim': 5, 'counter': 5, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.5b', 'multiplicity': 1, 'nt': [10, 34], 'qdim': 5, 'qvalues': [5, 5, -3, 1, 2, 1, 1, 0, 0, 2, 0, 0, -1, 0, 0, -2], 'schur_index': 1}
  • id: 4154777
    {'cdim': 3, 'counter': 2, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, -2, 0, 6, -2, 1, 1, 0, 0, 0, -2, 1, 1, 0], 'schur_index': 1}
  • id: 4154781
    {'cdim': 5, 'counter': 6, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.5c', 'multiplicity': 2, 'nt': [30, 217], 'qdim': 10, 'qvalues': [10, 10, -6, 2, -2, 2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 2], 'schur_index': 1}
  • id: 4154783
    {'cdim': 10, 'counter': 8, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.10a', 'multiplicity': 1, 'nt': [16, 1081], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 1, -2, -2, 0, 0, 1, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 4154784
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.10b', 'multiplicity': 1, 'nt': [20, 177], 'qdim': 10, 'qvalues': [10, 10, 2, -2, 1, -2, 2, 0, 0, 1, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 4154773
    {'cdim': 15, 'counter': 10, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.15a', 'multiplicity': 1, 'nt': [30, 214], 'qdim': 15, 'qvalues': [15, 15, -9, -1, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 4154782
    {'cdim': 8, 'counter': 7, 'faithful': True, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.8a', 'multiplicity': 2, 'nt': [32, 97742], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 4, 0, 0, 1, 1, -4, 0, 0, 0, -1, -1, 0], 'schur_index': 1}
  • id: 4154774
    {'cdim': 16, 'counter': 11, 'faithful': True, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.16a', 'multiplicity': 1, 'nt': [192, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -2, 0, 0, 1, 1, 2, 0, 0, 0, -1, -1, 0], 'schur_index': 2}
  • id: 4154775
    {'cdim': 20, 'counter': 12, 'faithful': False, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.20a', 'multiplicity': 1, 'nt': [40, 942], 'qdim': 20, 'qvalues': [20, 20, 4, 0, -1, -4, 0, 0, 0, -1, 1, 1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 4154776
    {'cdim': 24, 'counter': 13, 'faithful': True, 'group': '1920.241004', 'group_order': 1920, 'image': None, 'label': '1920.241004.24a', 'multiplicity': 1, 'nt': [80, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 6040632
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1920, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1920, 'label': '1920.241004.1a', '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]]]}
  • id: 6040640
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 2, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241004.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 6040641
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 3, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241004.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]]]}
  • id: 6040642
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 4, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241004.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6040643
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 5, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241004.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 6040644
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 6, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.5b', 'nt': [10, 34], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 6040645
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 7, 'cyclotomic_n': 3, 'dim': 5, 'faithful': False, 'field': [1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.5c1', 'nt': [30, 217], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040646
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 8, 'cyclotomic_n': 3, 'dim': 5, 'faithful': False, 'field': [1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.5c2', 'nt': [30, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040647
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 9, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241004', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241004.8a1', 'nt': [32, 97742], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]]]}
  • id: 6040633
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 10, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241004', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241004.8a2', 'nt': [32, 97742], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]]]}
  • id: 6040634
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 11, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.10a', 'nt': [16, 1081], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040635
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 12, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.10b', 'nt': [20, 177], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040636
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 13, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.15a', 'nt': [30, 214], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-9, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040637
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241004', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241004.16a', 'nt': [192, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 6040638
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241004.20a', 'nt': [40, 942], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 6040639
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '1920.241004', 'group_counter': 241004, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241004', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241004.24a', 'nt': [80, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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: 63520896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1920, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '1920.241004.1.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': True, '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': ['D', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1920.241004', 'subgroup_hash': 609720232146003705, 'subgroup_order': 1920, 'subgroup_tex': 'C_2.C_2^4:A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1920.241004.5.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': '384.617', 'subgroup_hash': 617, 'subgroup_order': 384, 'subgroup_tex': 'C_2.C_2\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '320.1582', 'subgroup_hash': 1582, 'subgroup_order': 320, 'subgroup_tex': 'C_2.C_2^4:D_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.10.a1.a1', 'maximal': False, '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': '192.1024', 'subgroup_hash': 1024, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.10.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.990', 'subgroup_hash': 990, 'subgroup_order': 192, 'subgroup_tex': 'D_4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.12.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.199', 'subgroup_hash': 199, 'subgroup_order': 160, 'subgroup_tex': 'C_2.C_2^4:C_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1920.241004.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.934', 'subgroup_hash': 934, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 2}
  • id: 63520973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.16.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 63520981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.20.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': '96.193', 'subgroup_hash': 193, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63520897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.67', 'subgroup_hash': 67, 'subgroup_order': 96, 'subgroup_tex': '\\Unitary(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.20.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': '96.202', 'subgroup_hash': 202, 'subgroup_order': 96, 'subgroup_tex': 'D_4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.36', 'subgroup_hash': 36, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63520909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1920.241004.60.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, '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': ['F', 'R', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 63520921
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63520927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63520934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.160.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63520943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63520944
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 63520945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520946
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 63520947
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 63520948
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.192.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 63520949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520963
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520964
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': 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: 63520965
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.320.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': 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: 63520966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1920.241004.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 63520967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63520968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63520969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63520970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': 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: 63520972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241004.480.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.f2.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 63520976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '1920.241004.640.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '640.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': 640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 63520977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 2, 'counter': 83, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1920.241004.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '960.11358', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11358, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 960, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:A_5', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'S', 'U0', 'C2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.960.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.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': 960, '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: 63520979
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241004.960.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.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': 960, '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: 63520980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241004', 'ambient_counter': 241004, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1920.241004.1920.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1920.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1920.241004', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 609720232146003705, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1920, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2.C_2^4:A_5', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C3'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 63520961
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.g1.a1', '120.i1.a1'], 'contains': ['480.e1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6224, -1, 6847, -1, 8103, -1, 6827, -1], 'generators': [186116097481241105902138803994165562, 243098267598049033227284485770698446, 214492074472297635153109037382860498], 'label': '1920.241004.240.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '240.k1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520896
    {'ambient': '1920.241004', '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': '960.a1.a1', 'complements': ['1920.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1', '6.a1.a1', '10.b1.a1', '16.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4824, 5000, 4439, 5000, 4458, 5000, 4268, 5000], 'generators': [192168987205119448116666385719888198, 138082694181804405008029966820908771, 43338244971230914875922057098785435, 34752607231971831205328187704670339, 128038124212295133726309154840670987, 152392397219130355401471868579141232, 227401078374797619721048963777087686], 'label': '1920.241004.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '960.11358', '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': '960.11358'}
  • id: 63520897
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.226', 'aut_weyl_index': 20, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.e1.a1', '60.g1.a1', '80.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1707, -1, 1336, -1, 1872, -1, 1393, -1], 'generators': [180095450461504941506467169935503463, 95260354422632527351378767121597110, 43338244971230914875922057098785435, 8297397713756767281590264476954474, 109596482832836913822183419304009050, 10861824984207935477454646981183435], 'label': '1920.241004.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '960.11358', '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': '48.48'}
  • id: 63520898
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.b1.a1'], 'contains': ['40.b1.a1', '40.e1.a1', '60.a1.a1', '80.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2928, -1, 2480, -1, 2808, -1, 2467, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 128038124212295133726309154840670987, 211473144322252758440208622907656227], 'label': '1920.241004.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '960.11358', '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': '96.195'}
  • id: 63520899
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.c1.a1', '60.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5042, -1, 4502, -1, 4911, -1, 3944, -1], 'generators': [138082694181804405008029966820908771, 69999103887714446488264850852568507, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 180612540482877988119729717375751433, 128038124212295133726309154840670987], 'label': '1920.241004.30.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': '960.11358', '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': '64.138'}
  • id: 63520900
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5879, -1, 5253, -1, 5979, -1, 5483, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.30.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': '30.b1.a1', 'projective_image': '960.11358', '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': '96.70'}
  • id: 63520901
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.e1.a1', '60.f1.a1', '60.g1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4042, -1, 3323, -1, 4078, -1, 3175, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 180612540482877988119729717375751433, 128038124212295133726309154840670987], 'label': '1920.241004.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '960.11358', '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': '64.138'}
  • id: 63520902
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '120.34', 'aut_weyl_index': 16, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1'], 'contains': ['160.d1.a1', '192.b1.a1', '320.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': '32T97742', 'count': 16, 'diagramx': [9759, -1, 9295, -1, 9889, -1, 9777, -1], 'generators': [82598457740633465794399072269993249, 235944997683916807329062730065520504], 'label': '1920.241004.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520903
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.b1.a1', '80.f1.a1', '80.f1.a2', '120.e1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8965, -1, 7772, -1, 7200, -1, 8071, -1], 'generators': [3457140556672896168213912340912589, 43338244971230914875922057098785435, 186116097481241105902138803994165562, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.40.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520904
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '20.c1.a1'], 'contains': ['80.e1.a1', '120.h1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3141, -1, 3525, -1, 4812, -1, 4378, -1], 'generators': [3457140556672896168213912340912589, 138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987], 'label': '1920.241004.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '40.b1.a1', 'projective_image': '960.11358', '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': '24.13'}
  • id: 63520905
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.g1.a1', '120.i1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6255, -1, 6486, -1, 7955, -1, 6926, -1], 'generators': [3457140556672896168213912340912589, 43338244971230914875922057098785435, 186116097481241105902138803994165562, 243098267598049033227284485770698446, 214492074472297635153109037382860498], 'label': '1920.241004.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '40.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520906
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '48.38', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '80.d1.a1', '120.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1130, -1, 669, -1, 1773, -1, 784, -1], 'generators': [180095450461504941506467169935503463, 43338244971230914875922057098785435, 147305144579507944151886965763259468, 152124193497589196252013037243685622, 49184152567654972198388205600926937], 'label': '1920.241004.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '40.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 63520907
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.5602', 'aut_weyl_index': 5, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '15.a1.a1', '20.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5042, -1, 3985, -1, 4755, -1, 4059, -1], 'generators': [138082694181804405008029966820908771, 69999103887714446488264850852568507, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 180612540482877988119729717375751433, 128038124212295133726309154840670987, 211473144322252758440208622907656227], 'label': '1920.241004.5.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': '960.11358', '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': '192.201'}
  • id: 63520908
    {'ambient': '1920.241004', 'aut_centralizer_order': 4, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.e1.a1', '120.k1.a1', '160.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1695, -1, 1484, -1, 1340, -1, 1329, -1], 'generators': [81487268975916121640880836577766147, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987, 8297397713756767281590264476954474], 'label': '1920.241004.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.e1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63520909
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1'], 'contains': ['80.e1.a1', '120.l1.a1', '160.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2102, -1, 1984, -1, 915, -1, 2882, -1], 'generators': [254832255301695241383329540747011506, 44558724122678859570675519529231413, 43338244971230914875922057098785435, 49935748411898969851850526685910663, 49184152567654972198388205600926937], 'label': '1920.241004.40.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '40.f1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63520910
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240996', 'aut_weyl_index': 1, 'centralizer': '960.a1.a1', 'complements': ['32.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.c1.a1', '30.c1.a1'], 'contains': ['120.h1.a1', '120.k1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4382, 5000, 3365, 5000, 3608, 5000, 3267, 5000], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 128038124212295133726309154840670987], 'label': '1920.241004.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': '60.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11358'}
  • id: 63520911
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.27', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.d1.a1', '120.f1.a1', '120.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5773, -1, 5126, -1, 6532, -1, 5323, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 247053627368392342897719775893863996, 49935748411898969851850526685910663, 234133971946284704092938837128729189], 'label': '1920.241004.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.b1.a1', 'projective_image': '960.11358', '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': '16.14'}
  • id: 63520912
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.138', 'aut_weyl_index': 30, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.c1.a1', '120.f1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4789, -1, 4396, -1, 5435, -1, 4953, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987, 202499290558413018023919597533838014], 'label': '1920.241004.60.c1.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': '60.c1.a1', 'projective_image': '960.11358', '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': '32.27'}
  • id: 63520913
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.27', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6705, -1, 5597, -1, 5983, -1, 5829, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 247053627368392342897719775893863996, 49935748411898969851850526685910663, 202499290558413018023919597533838014], 'label': '1920.241004.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.d1.a1', 'projective_image': '960.11358', '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': '16.14'}
  • id: 63520914
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1'], 'contains': ['120.g1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2991, -1, 3953, -1, 4111, -1, 3731, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 180612540482877988119729717375751433, 128038124212295133726309154840670987], 'label': '1920.241004.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '960.11358', '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': '64.138'}
  • id: 63520915
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.226', 'aut_weyl_index': 30, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '30.c1.a1'], 'contains': ['120.c1.a1', '120.g1.a1', '120.j1.a1', '120.k1.a1', '120.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1454, -1, 2422, -1, 2511, -1, 1915, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 8297397713756767281590264476954474, 109596482832836913822183419304009050, 170252726847701145030673469788942680], 'label': '1920.241004.60.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': '960.11358', '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': '32.27'}
  • id: 63520916
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.46', 'aut_weyl_index': 60, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '30.c1.a1'], 'contains': ['120.f1.a1', '120.g1.a1', '120.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3552, -1, 2894, -1, 3060, -1, 2421, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 180612540482877988119729717375751433, 8297397713756767281590264476954474, 109596482832836913822183419304009050], 'label': '1920.241004.60.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': '60.g1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 63520917
    {'ambient': '1920.241004', 'aut_centralizer_order': 3, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '40.d1.a1'], 'contains': ['160.a1.a1', '160.c1.a1', '240.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2142, -1, 674, -1, 2210, -1, 723, -1], 'generators': [43338244971230914875922057098785435, 104818605416313014996511468357148339, 109596482832836913822183419304009050, 211473144322252758440208622907656227], 'label': '1920.241004.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.a1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520918
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '30.c1.a1', '96.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4603, -1, 5405, -1, 4136, -1, 4614, -1], 'generators': [154161152621539872204890159388373417, 138082694181804405008029966820908771, 32985942750654531631844783627614244, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 128038124212295133726309154840670987], 'label': '1920.241004.6.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.234'}
  • id: 63520919
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1'], 'contains': ['160.d1.a1', '240.f1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9609, -1, 8672, -1, 8548, -1, 8353, -1], 'generators': [3457140556672896168213912340912589, 3466287220660971825998713317742931, 43338244971230914875922057098785435, 44376705521597528380868478227602073], 'label': '1920.241004.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '960.11358', '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': '12.3'}
  • id: 63520920
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '48.38', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '40.d1.a1'], 'contains': ['160.b1.a1', '160.c1.a1', '240.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3944, -1, 1212, -1, 528, -1, 1432, -1], 'generators': [180095450461504941506467169935503463, 43338244971230914875922057098785435, 147305144579507944151886965763259468, 49184152567654972198388205600926937], 'label': '1920.241004.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.c1.a1', 'projective_image': '960.11358', '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': '24.8'}
  • id: 63520921
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.14', 'aut_weyl_index': 80, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '40.d1.a1'], 'contains': ['160.c1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [146, -1, 131, -1, 153, -1, 141, -1], 'generators': [108456211334829316556397578005498195, 180095450461504941506467169935503463, 95260354422632527351378767121597110, 43338244971230914875922057098785435], 'label': '1920.241004.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63520922
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '40.e1.a1', '40.f1.a1'], 'contains': ['240.h1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1398, -1, 1665, -1, 1295, -1, 2871, -1], 'generators': [3457140556672896168213912340912589, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987], 'label': '1920.241004.80.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.e1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520923
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '12.3', 'aut_weyl_index': 160, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1'], 'contains': ['160.d1.a1', '240.j1.a1', '320.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9075, -1, 8193, -1, 9105, -1, 8867, -1], 'generators': [3457140556672896168213912340912589, 247053627368392342897719775893863996, 34840817839119653689611862920261606, 202499290558413018023919597533838014], 'label': '1920.241004.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '80.f1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520924
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '12.3', 'aut_weyl_index': 160, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1'], 'contains': ['160.d1.a1', '240.j1.a2', '320.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9075, -1, 7442, -1, 9105, -1, 9381, -1], 'generators': [241022587579438488499826580128058564, 3457140556672896168213912340912589, 186116097481241105902138803994165562, 224307670145208228607656332714372421], 'label': '1920.241004.80.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '80.f1.a2', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520925
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1'], 'contains': ['240.k1.a1', '320.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7380, -1, 6914, -1, 9563, -1, 7931, -1], 'generators': [3457140556672896168213912340912589, 233762301975969148689850650142407234, 186116097481241105902138803994165562, 252512359848922963447297260833472643], 'label': '1920.241004.80.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '80.g1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520926
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '16.a1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.b2.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8179, -1, 9479, -1, 7093, -1, 9842, -1], 'generators': [115321250433428211278545486894691792, 43338244971230914875922057098785435, 156696964739376105897292330676825562], 'label': '1920.241004.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '960.11358', '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': '10.1'}
  • id: 63520927
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5192, -1, 4580, -1, 5307, -1, 4900, -1], 'generators': [138082694181804405008029966820908771, 254832255301695241383329540747011506, 43338244971230914875922057098785435, 202499290558413018023919597533838014], 'label': '1920.241004.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520928
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 120, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5192, -1, 4980, -1, 5307, -1, 5330, -1], 'generators': [43338244971230914875922057098785435, 128038124212295133726309154840670987, 202499290558413018023919597533838014, 235936166935039335846948936260810987], 'label': '1920.241004.120.a1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.a1.a2', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520929
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.b1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6188, -1, 5253, -1, 5979, -1, 5483, -1], 'generators': [3457140556672896168213912340912589, 138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.10.a1.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': '10.a1.a1', 'projective_image': '960.11358', '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': '96.70'}
  • id: 63520930
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.27', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6179, -1, 5381, -1, 6247, -1, 5761, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 202499290558413018023919597533838014, 214492074472297635153109037382860498], 'label': '1920.241004.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.b1.a1', 'projective_image': '960.11358', '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': '16.14'}
  • id: 63520931
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.138', 'aut_weyl_index': 30, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.d1.a1', '60.f1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4244, -1, 4137, -1, 4293, -1, 3819, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 49935748411898969851850526685910663, 202499290558413018023919597533838014], 'label': '1920.241004.120.c1.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': '120.c1.a1', 'projective_image': '960.11358', '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': '32.27'}
  • id: 63520932
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.27', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7128, -1, 5823, -1, 6763, -1, 6236, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 243098267598049033227284485770698446, 247053627368392342897719775893863996], 'label': '1920.241004.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.d1.a1', 'projective_image': '960.11358', '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': '16.14'}
  • id: 63520933
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.f1.a1', '240.j1.a1', '240.j1.a2'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8763, -1, 8048, -1, 7373, -1, 7611, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.120.e1.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': '120.e1.a1', 'projective_image': '960.11358', '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': '12.3'}
  • id: 63520934
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.g1.a1'], 'contains': ['240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3809, -1, 3748, -1, 4903, -1, 4238, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 49935748411898969851850526685910663, 234133971946284704092938837128729189], 'label': '1920.241004.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.f1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520935
    {'ambient': '1920.241004', 'aut_centralizer_order': 4, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.b1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1588, -1, 2937, -1, 3237, -1, 2517, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 180612540482877988119729717375751433, 49935748411898969851850526685910663], 'label': '1920.241004.120.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': '960.11358', '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': '16.11'}
  • id: 63520936
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '60.a1.a1', '60.c1.a1', '60.e1.a1'], 'contains': ['240.b1.a1', '240.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2710, -1, 3358, -1, 3728, -1, 3297, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987], 'label': '1920.241004.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '960.11358', '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': '96.70'}
  • id: 63520937
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.227', 'aut_weyl_index': 20, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '60.b1.a1'], 'contains': ['240.c1.a1', '240.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5685, -1, 6716, -1, 7827, -1, 6758, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 243098267598049033227284485770698446, 214492074472297635153109037382860498], 'label': '1920.241004.120.i1.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': '120.i1.a1', 'projective_image': '960.11358', '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': '48.50'}
  • id: 63520938
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '60.f1.a1'], 'contains': ['240.d1.a1', '240.e1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [707, -1, 1151, -1, 1621, -1, 1123, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 180612540482877988119729717375751433, 152124193497589196252013037243685622], 'label': '1920.241004.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '120.j1.a1', 'projective_image': '960.11358', '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': '16.11'}
  • id: 63520939
    {'ambient': '1920.241004', 'aut_centralizer_order': 4, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '60.a1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.b1.a1', '240.d1.a1', '240.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3165, -1, 2596, -1, 2841, -1, 2151, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 128038124212295133726309154840670987, 8297397713756767281590264476954474], 'label': '1920.241004.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '960.11358', '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': '48.48'}
  • id: 63520940
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.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', '40.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2670, -1, 2002, -1, 2610, -1, 2193, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 128038124212295133726309154840670987, 49184152567654972198388205600926937, 193141276061521750491496457592526579], 'label': '1920.241004.10.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '10.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 63520941
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.f1.a1', '60.f1.a1'], 'contains': ['240.e1.a1', '240.g1.a1', '240.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [371, -1, 2126, -1, 915, -1, 1789, -1], 'generators': [75649266821348557454529924162103733, 43338244971230914875922057098785435, 49935748411898969851850526685910663, 162005789556935906662130756570176683], 'label': '1920.241004.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '120.l1.a1', 'projective_image': '960.11358', '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': '16.11'}
  • id: 63520942
    {'ambient': '1920.241004', 'aut_centralizer_order': 6, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '80.a1.a1'], 'contains': ['320.a1.a1', '320.b1.a1', '480.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [4741, -1, 6270, -1, 5274, -1, 5844, -1], 'generators': [3457140556672896168213912340912589, 43338244971230914875922057098785435, 186116097481241105902138803994165562], 'label': '1920.241004.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520943
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '12.4', 'aut_weyl_index': 160, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.f1.a1', '80.c1.a1'], 'contains': ['320.a1.a1', '320.c1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [6773, -1, 2334, -1, 2668, -1, 6240, -1], 'generators': [44558724122678859570675519529231413, 43338244971230914875922057098785435, 49184152567654972198388205600926937], 'label': '1920.241004.160.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.c1.a1', 'old_label': '160.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63520944
    {'ambient': '1920.241004', 'aut_centralizer_order': 12, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '80.a1.a1', '80.c1.a1', '80.d1.a1'], 'contains': ['320.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1888, -1, 553, -1, 763, -1, 1104, -1], 'generators': [43338244971230914875922057098785435, 100572719201808410636639370632583780, 104818605416313014996511468357148339], 'label': '1920.241004.160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '160.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520945
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.b1.a1', '80.f1.a1', '80.f1.a2'], 'contains': ['480.f1.a1', '640.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9719, -1, 8810, -1, 8878, -1, 8871, -1], 'generators': [3457140556672896168213912340912589, 3466287220660971825998713317742931, 268618014511249353477082218350256], 'label': '1920.241004.160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '160.d1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520946
    {'ambient': '1920.241004', 'aut_centralizer_order': 5, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '96.a1.a1'], 'contains': ['384.a1.a1', '960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7918, -1, 9331, -1, 6124, -1, 9263, -1], 'generators': [154161152621539872204890159388373417, 43338244971230914875922057098785435], 'label': '1920.241004.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520947
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '96.a1.a1'], 'contains': ['384.a1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9736, -1, 9869, -1, 8359, -1, 9842, -1], 'generators': [68130094326287647968434564611305728, 256471155224680852241061445285329060], 'label': '1920.241004.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63520948
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '192.b2', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1'], 'contains': ['384.a1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8835, -1, 9614, -1, 7089, -1, 9568, -1], 'generators': [156696964739376105897292330676825562, 256471155224680852241061445285329060], 'label': '1920.241004.192.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '192.b2.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b2.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63520949
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.d1.a1', '480.d1.a2'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6828, -1, 5760, -1, 5724, -1, 6533, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 202499290558413018023919597533838014], 'label': '1920.241004.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.a1.a1', 'projective_image': '960.11358', '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': '4.2'}
  • id: 63520950
    {'ambient': '1920.241004', 'aut_centralizer_order': 16, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.c1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1', '120.k1.a1'], 'contains': ['480.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3659, -1, 3762, -1, 4008, -1, 3819, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 49935748411898969851850526685910663], 'label': '1920.241004.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520951
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['60.a1.a1', '192.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4603, -1, 6157, -1, 3381, -1, 4656, -1], 'generators': [154161152621539872204890159388373417, 138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 128038124212295133726309154840670987], 'label': '1920.241004.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '960.11358', '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': '160.234'}
  • id: 63520952
    {'ambient': '1920.241004', 'aut_centralizer_order': 16, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.d1.a1', '120.f1.a1', '120.i1.a1'], 'contains': ['480.a1.a1', '480.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5812, -1, 4952, -1, 6173, -1, 5327, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562, 243098267598049033227284485770698446], 'label': '1920.241004.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.c1.a1', 'projective_image': '960.11358', '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': '4.2'}
  • id: 63520953
    {'ambient': '1920.241004', 'aut_centralizer_order': 24, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '80.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '120.j1.a1', '120.k1.a1'], 'contains': ['480.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2406, -1, 1204, -1, 2371, -1, 1831, -1], 'generators': [43338244971230914875922057098785435, 227401078374797619721048963777087686, 152124193497589196252013037243685622], 'label': '1920.241004.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520954
    {'ambient': '1920.241004', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '120.c1.a1', '120.j1.a1', '120.l1.a1'], 'contains': ['480.b1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2691, -1, 1735, -1, 1621, -1, 2105, -1], 'generators': [43338244971230914875922057098785435, 49935748411898969851850526685910663, 202499290558413018023919597533838014], 'label': '1920.241004.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '240.e1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520955
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 320, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '120.e1.a1'], 'contains': ['480.b1.a1', '480.f1.a1', '480.f2.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9767, -1, 8066, -1, 7447, -1, 7539, -1], 'generators': [43338244971230914875922057098785435, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '240.f1.a1', 'projective_image': '960.11358', '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': '3.1'}
  • id: 63520956
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '240.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1.a1', '120.g1.a1', '120.j1.a1', '120.l1.a1'], 'contains': ['480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [613, -1, 1474, -1, 1324, -1, 1557, -1], 'generators': [43338244971230914875922057098785435, 162523794940251714119032201685802610, 49935748411898969851850526685910663], 'label': '1920.241004.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '240.g1.a1', 'projective_image': '960.11358', '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': '4.2'}
  • id: 63520957
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1.a1', '120.h1.a1', '120.k1.a1', '120.l1.a1'], 'contains': ['480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2106, -1, 2820, -1, 1917, -1, 2380, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435, 227401078374797619721048963777087686], 'label': '1920.241004.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '240.h1.a1', 'projective_image': '960.11358', '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': '24.12'}
  • id: 63520958
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1'], 'contains': ['480.d1.a1', '480.d1.a2', '480.e1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7432, -1, 6301, -1, 6759, -1, 7246, -1], 'generators': [186116097481241105902138803994165562, 243098267598049033227284485770698446, 247053627368392342897719775893863996], 'label': '1920.241004.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.d1.a1', 'old_label': '240.i1.a1', 'projective_image': '1920.241004', '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': '4.2'}
  • id: 63520959
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '3.1', 'aut_weyl_index': 640, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '120.e1.a1'], 'contains': ['480.d1.a1', '480.f1.a1', '480.f2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9388, -1, 8491, -1, 7785, -1, 7851, -1], 'generators': [247053627368392342897719775893863996, 34840817839119653689611862920261606, 202499290558413018023919597533838014], 'label': '1920.241004.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '240.j1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63520960
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '3.1', 'aut_weyl_index': 640, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a2', '120.e1.a1'], 'contains': ['480.d1.a2', '480.f1.a1', '480.f2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9388, -1, 7775, -1, 7785, -1, 8163, -1], 'generators': [186116097481241105902138803994165562, 247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.240.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '240.j1.a2', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63520962
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.5602', 'aut_weyl_index': 5, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5042, -1, 4325, -1, 4849, -1, 3986, -1], 'generators': [138082694181804405008029966820908771, 69999103887714446488264850852568507, 43338244971230914875922057098785435, 227401078374797619721048963777087686, 192168987205119448116666385719888198, 180612540482877988119729717375751433, 128038124212295133726309154840670987], 'label': '1920.241004.15.a1.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.a1.a1', 'projective_image': '960.11358', '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': '192.201'}
  • id: 63520963
    {'ambient': '1920.241004', 'aut_centralizer_order': 24, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '80.e1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1'], 'contains': ['640.a1.a1', '960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [5796, -1, 4095, -1, 5117, -1, 6240, -1], 'generators': [3457140556672896168213912340912589, 43338244971230914875922057098785435], 'label': '1920.241004.320.a1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '320.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520964
    {'ambient': '1920.241004', 'aut_centralizer_order': 6, 'aut_label': '320.b1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '80.f1.a2', '80.g1.a1', '160.a1.a1'], 'contains': ['640.a1.a1', '960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [7598, -1, 7042, -1, 8062, -1, 8391, -1], 'generators': [3457140556672896168213912340912589, 186116097481241105902138803994165562], 'label': '1920.241004.320.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.a1.a1', 'old_label': '320.b1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520965
    {'ambient': '1920.241004', 'aut_centralizer_order': 2, 'aut_label': '320.c1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '6.1', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '160.b1.a1'], 'contains': ['640.a1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [8198, -1, 7566, -1, 8656, -1, 8666, -1], 'generators': [49184152567654972198388205600926937, 371670529374669933157217012116366], 'label': '1920.241004.320.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.b1.a1', 'old_label': '320.c1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520966
    {'ambient': '1920.241004', 'aut_centralizer_order': 5, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.b2.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8677, -1, 9635, -1, 7089, -1, 9416, -1], 'generators': [154161152621539872204890159388373417], 'label': '1920.241004.384.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520967
    {'ambient': '1920.241004', 'aut_centralizer_order': 192, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.a1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '240.d1.a1'], 'contains': ['960.a1.a1', '960.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5627, -1, 5459, -1, 5435, -1, 5844, -1], 'generators': [43338244971230914875922057098785435, 186116097481241105902138803994165562], 'label': '1920.241004.480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '960.11358', '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: 63520968
    {'ambient': '1920.241004', 'aut_centralizer_order': 16, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.b1.a1', '240.a1.a1', '240.e1.a1', '240.f1.a1'], 'contains': ['960.a1.a1', '960.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7215, -1, 5862, -1, 5773, -1, 6849, -1], 'generators': [43338244971230914875922057098785435, 202499290558413018023919597533838014], 'label': '1920.241004.480.b1.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '480.b1.a1', 'projective_image': '960.11358', '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: 63520969
    {'ambient': '1920.241004', 'aut_centralizer_order': 96, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '20.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.c1.a1', '240.b1.a1', '240.d1.a1', '240.e1.a1', '240.g1.a1', '240.h1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2406, -1, 1735, -1, 1917, -1, 2105, -1], 'generators': [138082694181804405008029966820908771, 43338244971230914875922057098785435], 'label': '1920.241004.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '480.c1.a1', 'projective_image': '960.11358', '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: 63520970
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.i1.a1', '240.j1.a1'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8352, -1, 6472, -1, 6474, -1, 7162, -1], 'generators': [34840817839119653689611862920261606, 202499290558413018023919597533838014], 'label': '1920.241004.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '480.d1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520971
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.i1.a1', '240.j1.a2'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8352, -1, 6762, -1, 6474, -1, 7474, -1], 'generators': [186116097481241105902138803994165562, 202499290558413018023919597533838014], 'label': '1920.241004.480.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '480.d1.a2', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520972
    {'ambient': '1920.241004', 'aut_centralizer_order': 16, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '240.i1.a1', '240.k1.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6507, -1, 6185, -1, 6792, -1, 6556, -1], 'generators': [186116097481241105902138803994165562, 243098267598049033227284485770698446], 'label': '1920.241004.480.e1.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': '480.e1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520973
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '120.34', 'aut_weyl_index': 16, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['32.a1.a1', '80.b1.a1', '96.a1.a1', '160.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8226, -1, 9018, -1, 8664, -1, 9777, -1], 'generators': [82598457740633465794399072269993249, 43338244971230914875922057098785435, 235944997683916807329062730065520504], 'label': '1920.241004.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520974
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 320, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.d1.a1', '240.f1.a1', '240.j1.a1', '240.j1.a2'], 'contains': ['960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9854, -1, 8165, -1, 7744, -1, 8098, -1], 'generators': [241022587579438488499826580128058564, 202499290558413018023919597533838014], 'label': '1920.241004.480.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '480.f1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63520975
    {'ambient': '1920.241004', 'aut_centralizer_order': 8, 'aut_label': '480.f2', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.f1.a1', '240.j1.a1', '240.j1.a2'], 'contains': ['960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9467, -1, 8732, -1, 7406, -1, 7786, -1], 'generators': [247053627368392342897719775893863996, 202499290558413018023919597533838014], 'label': '1920.241004.480.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.e1.a1', 'old_label': '480.f2.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520976
    {'ambient': '1920.241004', 'aut_centralizer_order': 24, 'aut_label': '640.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.d1.a1', '320.a1.a1', '320.b1.a1', '320.c1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7796, -1, 7421, -1, 8062, -1, 8391, -1], 'generators': [3457140556672896168213912340912589], 'label': '1920.241004.640.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '640.a1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '640.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520977
    {'ambient': '1920.241004', 'aut_centralizer_order': 1920, 'aut_label': '960.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1'], 'contains': ['1920.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6445, 5000, 5629, 5000, 5604, 5000, 6545, 5000], 'generators': [43338244971230914875922057098785435], 'label': '1920.241004.960.a1.a1', 'mobius_quo': -1, 'mobius_sub': 960, 'normal_closure': '960.a1.a1', 'normal_contained_in': ['60.a1.a1'], 'normal_contains': ['1920.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': '1.1', 'quotient_action_kernel': '960.11358', 'quotient_action_kernel_order': 960, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520978
    {'ambient': '1920.241004', 'aut_centralizer_order': 192, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.b1.a1', '480.a1.a1', '480.d1.a1', '480.d1.a2', '480.e1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7515, -1, 6511, -1, 6792, -1, 7318, -1], 'generators': [186116097481241105902138803994165562], 'label': '1920.241004.960.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '960.b1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520979
    {'ambient': '1920.241004', 'aut_centralizer_order': 16, 'aut_label': '960.c1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '120.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.b2.a1', '320.c1.a1', '480.b1.a1', '480.d1.a1', '480.d1.a2', '480.f1.a1', '480.f2.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8989, -1, 7655, -1, 7398, -1, 7942, -1], 'generators': [202499290558413018023919597533838014], 'label': '1920.241004.960.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.e1.a1', 'old_label': '960.c1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520980
    {'ambient': '1920.241004', 'aut_centralizer_order': None, 'aut_label': '1920.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': ['384.a1.a1', '640.a1.a1', '960.a1.a1', '960.b1.a1', '960.c1.a1'], 'contains': [], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7796, 5000, 7421, 5000, 7089, 5000, 7942, 5000], 'generators': [], 'label': '1920.241004.1920.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1920.a1.a1', 'normal_contained_in': ['960.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1920.a1.a1', 'projective_image': '1920.241004', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1920.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520981
    {'ambient': '1920.241004', 'aut_centralizer_order': 1, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.e1.a1', '40.f1.a1', '60.f1.a1', '80.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2351, -1, 1760, -1, 1340, -1, 1915, -1], 'generators': [180095450461504941506467169935503463, 43338244971230914875922057098785435, 8297397713756767281590264476954474, 109596482832836913822183419304009050, 10861824984207935477454646981183435, 49184152567654972198388205600926937], 'label': '1920.241004.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.a1.a1', 'projective_image': '960.11358', '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': '96.195'}