Abstract group data - 1920.240999

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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': 2, 'aut_exponent': 120, 'aut_gen_orders': [10, 12], 'aut_gens': [[5880454084857204622206, 347541499243366980819838], [284435607306449572783511, 451835442963471196742542], [465275427339289864827054, 195599220745617572693756]], 'aut_group': '7680.x', 'aut_hash': 4264655218017036024, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7680, 'aut_permdeg': 120, 'aut_perms': [3365351623480908461248708671676214690036833033986869784948516923910976235244218952867541768320994897750174110476107679566975127823982918169522287718165571863348340540437702998417084746319795932321119, 93217527004387808084908652195371258344212532680782750947640635423112421687531829594632758524975345128804210536705120189424062881991193465909897183568340832229781993778805930116378884418950062809020], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 15, 1, 2], [3, 320, 1, 1], [4, 60, 4, 1], [4, 120, 1, 2], [5, 192, 2, 1], [6, 320, 1, 1], [10, 192, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6: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': '7680.x', 'autcentquo_hash': 4264655218017036024, 'autcentquo_nilpotent': False, 'autcentquo_order': 7680, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6:S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 15, 2], [3, 320, 1], [4, 60, 4], [4, 120, 2], [5, 192, 2], [6, 320, 1], [10, 192, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '960.11357', 'commutator_count': 1, 'commutator_label': '1920.240999', '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': 240999, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 15, 1, 2], [3, 320, 1, 1], [4, 60, 2, 2], [4, 120, 1, 2], [5, 192, 2, 1], [6, 320, 1, 1], [10, 192, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 228, 'exponent': 60, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 0, 2], [10, 0, 2], [12, -1, 2], [20, -1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '960.11357', 'hash': 240999, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [5, 3], 'inner_gens': [[5880454084857204622206, 284051000923412665318134], [319396811347132045390673, 347541499243366980819838]], 'inner_hash': 11357, 'inner_nilpotent': False, 'inner_order': 960, 'inner_split': True, 'inner_tex': 'C_2^4:A_5', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 1], [3, 2], [4, 1], [5, 1], [6, 2], [10, 2], [12, 2], [15, 4], [20, 1]], 'label': '1920.240999', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 1, 'linQ_dim': 12, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2^5.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': 11, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 16, 'number_divisions': 12, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 87, 'number_subgroup_classes': 121, 'number_subgroups': 3730, 'old_label': None, 'order': 1920, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 320], [4, 480], [5, 384], [6, 320], [10, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1586624263563968398080, 248483103256894241998673], [438299409872627280507049, 329772058109049988375063]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [16, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': True, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [5, 1], [6, 1], [12, 1], [15, 4], [20, 2], [24, 1]], 'representations': {'Perm': {'d': 24, 'gens': [5880454084857204622206, 347541499243366980819838]}}, 'schur_multiplier': [4, 4], 'semidirect_product': False, '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_2^5.A_5', 'transitive_degree': 24, '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: 109132866
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 240999, 'group_order': 1920, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109132874
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 240999, 'group_order': 1920, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 81132435459866835843247, 'size': 1}
  • id: 109132875
    {'aut_label': '2B', 'centralizer': '15.a1.a1', 'counter': 3, 'group_counter': 240999, 'group_order': 1920, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 81030253868094248489527, 'size': 15}
  • id: 109132876
    {'aut_label': '2C', 'centralizer': '15.a1.a1', 'counter': 4, 'group_counter': 240999, 'group_order': 1920, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 3425526112872750163206, 'size': 15}
  • id: 109132877
    {'aut_label': '3A', 'centralizer': '320.a1.a1', 'counter': 5, 'group_counter': 240999, 'group_order': 1920, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 370743860402273267274372, 'size': 320}
  • id: 109132878
    {'aut_label': '4A1', 'centralizer': '60.e1.a1', 'counter': 6, 'group_counter': 240999, 'group_order': 1920, 'label': '4A1', 'order': 4, 'powers': [3, 7, 6], 'representative': 435384592201945419194143, 'size': 60}
  • id: 109132879
    {'aut_label': '4A1', 'centralizer': '60.e1.a1', 'counter': 7, 'group_counter': 240999, 'group_order': 1920, 'label': '4A-1', 'order': 4, 'powers': [3, 6, 7], 'representative': 462360616070969374256136, 'size': 60}
  • id: 109132880
    {'aut_label': '4A1', 'centralizer': '60.e1.b1', 'counter': 8, 'group_counter': 240999, 'group_order': 1920, 'label': '4B1', 'order': 4, 'powers': [3, 9, 8], 'representative': 333657624013157525309449, 'size': 60}
  • id: 109132881
    {'aut_label': '4A1', 'centralizer': '60.e1.b1', 'counter': 9, 'group_counter': 240999, 'group_order': 1920, 'label': '4B-1', 'order': 4, 'powers': [3, 8, 9], 'representative': 384184132918976092825830, 'size': 60}
  • id: 109132867
    {'aut_label': '4C', 'centralizer': '120.f1.a1', 'counter': 10, 'group_counter': 240999, 'group_order': 1920, 'label': '4C', 'order': 4, 'powers': [4, 10, 10], 'representative': 488884199689502040331490, 'size': 120}
  • id: 109132868
    {'aut_label': '4D', 'centralizer': '120.g1.a1', 'counter': 11, 'group_counter': 240999, 'group_order': 1920, 'label': '4D', 'order': 4, 'powers': [2, 11, 11], 'representative': 202908615572514991000062, 'size': 120}
  • id: 109132869
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 12, 'group_counter': 240999, 'group_order': 1920, 'label': '5A1', 'order': 5, 'powers': [13, 13, 1], 'representative': 516624299119011269499109, 'size': 192}
  • id: 109132870
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 13, 'group_counter': 240999, 'group_order': 1920, 'label': '5A2', 'order': 5, 'powers': [12, 12, 1], 'representative': 183949913172074834574016, 'size': 192}
  • id: 109132871
    {'aut_label': '6A', 'centralizer': '320.a1.a1', 'counter': 14, 'group_counter': 240999, 'group_order': 1920, 'label': '6A', 'order': 6, 'powers': [5, 2, 14], 'representative': 226346923924963018639495, 'size': 320}
  • id: 109132872
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 15, 'group_counter': 240999, 'group_order': 1920, 'label': '10A1', 'order': 10, 'powers': [12, 16, 2], 'representative': 138472235549705217813096, 'size': 192}
  • id: 109132873
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 16, 'group_counter': 240999, 'group_order': 1920, 'label': '10A3', 'order': 10, 'powers': [13, 15, 2], 'representative': 537218388643591048659886, 'size': 192}
• 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: 4154719
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.1a', '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: 4154724
    {'cdim': 4, 'counter': 3, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 4154725
    {'cdim': 5, 'counter': 4, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, 5, -1, 1, 1, 1, 1, 1, 1, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 4154723
    {'cdim': 3, 'counter': 2, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, -2, -2, -2, -2, -2, -2, 1, 1, 0, 1, 1], 'schur_index': 1}
  • id: 4154726
    {'cdim': 6, 'counter': 5, 'faithful': True, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.6a', 'multiplicity': 2, 'nt': [24, 4945], 'qdim': 12, 'qvalues': [12, -12, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, -2], 'schur_index': 1}
  • id: 4154729
    {'cdim': 15, 'counter': 8, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.15a', 'multiplicity': 1, 'nt': [16, 1080], 'qdim': 15, 'qvalues': [15, 15, -1, -1, 0, -1, -1, -1, -1, -1, 3, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4154730
    {'cdim': 15, 'counter': 9, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.15b', 'multiplicity': 1, 'nt': [20, 176], 'qdim': 15, 'qvalues': [15, 15, -1, -1, 0, -1, -1, -1, -1, 3, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4154720
    {'cdim': 15, 'counter': 10, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.15c', 'multiplicity': 1, 'nt': [20, 176], 'qdim': 15, 'qvalues': [15, 15, -1, -1, 0, -1, -1, 3, 3, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4154721
    {'cdim': 15, 'counter': 11, 'faithful': False, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.15d', 'multiplicity': 1, 'nt': [20, 176], 'qdim': 15, 'qvalues': [15, 15, -1, -1, 0, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4154727
    {'cdim': 10, 'counter': 6, 'faithful': True, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.10a', 'multiplicity': 2, 'nt': [40, 1579], 'qdim': 20, 'qvalues': [20, -20, 4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 4154722
    {'cdim': 20, 'counter': 12, 'faithful': True, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.20a', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 20, 'qvalues': [20, -20, 4, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], 'schur_index': 2}
  • id: 4154728
    {'cdim': 12, 'counter': 7, 'faithful': True, 'group': '1920.240999', 'group_order': 1920, 'image': None, 'label': '1920.240999.12a', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 24, 'qvalues': [24, -24, -8, 8, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 1], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 6040563
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1920, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1920, 'label': '1920.240999.1a', '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: 6040571
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 2, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.240999.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6040572
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 3, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.240999.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6040573
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 4, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.240999.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6040574
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 5, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.240999.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040575
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 6, 'cyclotomic_n': 4, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': 0, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.6a1', 'nt': [24, 4945], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6040576
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 7, 'cyclotomic_n': 4, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': 0, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.6a2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6040577
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 8, 'cyclotomic_n': 4, 'dim': 10, 'faithful': True, 'field': [1, 0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': 0, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.10a1', 'nt': [40, 1579], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040578
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 9, 'cyclotomic_n': 4, 'dim': 10, 'faithful': True, 'field': [1, 0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': 0, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.10a2', 'nt': [40, 2], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040564
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 10, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.12a1', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6040565
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 11, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.12a2', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6040566
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 12, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11357', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.240999.15a', 'nt': [16, 1080], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040567
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 13, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11357', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.240999.15b', 'nt': [20, 176], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040568
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11357', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.240999.15c', 'nt': [20, 176], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040569
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11357', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.240999.15d', 'nt': [20, 176], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040570
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '1920.240999', 'group_counter': 240999, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.240999', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.240999.20a', 'nt': [120, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 63520512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1920, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '1920.240999.1.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': '1920.240999', 'subgroup_hash': 2717355043640295321, 'subgroup_order': 1920, 'subgroup_tex': 'C_2^5.A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1920.240999.5.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': '384.5864', 'subgroup_hash': 5864, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.6.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': '320.1583', 'subgroup_hash': 1583, 'subgroup_order': 320, 'subgroup_tex': 'C_2^5.D_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.10.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '160.235', 'subgroup_hash': 235, 'subgroup_order': 160, 'subgroup_tex': 'C_2\\wr C_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1920.240999.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1468', 'subgroup_hash': 1468, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 2}
  • id: 63520600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.16.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': 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': 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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 63520611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.16.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a2', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 63520622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.16.a1.a3', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a3', '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': 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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 63520513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.16.a1.a4', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a4', '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': 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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 63520524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63520535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, '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': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63520538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.20.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': '96.3', 'subgroup_hash': 3, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.20.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': '96.203', 'subgroup_hash': 203, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.49', 'subgroup_hash': 49, 'subgroup_order': 80, 'subgroup_tex': 'C_2^4:C_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.30.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': '64.74', 'subgroup_hash': 74, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.30.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': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.30.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': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, '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': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63520552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.b1', 'outer_equivalence': False, 'perfect': False, '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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63520553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1920.240999.60.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 63520555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.b1', 'outer_equivalence': False, 'perfect': False, '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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.e1.b1', 'outer_equivalence': False, 'perfect': False, '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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.h1.b1', 'outer_equivalence': False, 'perfect': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.i1.b1', 'outer_equivalence': False, 'perfect': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.a2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a2.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.a2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a2.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: 63520574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.a3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a3.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.b1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1.a3', 'outer_equivalence': False, 'perfect': False, '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: 63520579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.80.b1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1.a4', 'outer_equivalence': False, 'perfect': False, '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: 63520580
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.96.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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.b1', 'outer_equivalence': False, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63520592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.i1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.j1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63520601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63520602
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.160.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 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: 63520605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.160.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.192.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: 63520608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.a1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.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: 63520612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.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: 63520613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c2.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d2.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.d2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d2.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: 63520618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.d3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d3.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.e1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a3', 'outer_equivalence': False, 'perfect': False, '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: 63520623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.e1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a4', 'outer_equivalence': False, 'perfect': False, '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: 63520624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.f1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.g1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.g1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.240.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.k2.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520516
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.320.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: 63520517
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1920.240999.384.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: 63520518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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: 63520519
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.c2.a1', 'outer_equivalence': False, 'perfect': False, '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: 63520522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520523
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.480.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.b1', 'outer_equivalence': False, 'perfect': False, '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: 63520525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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: 63520528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.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: 63520529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.480.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 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: 63520531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.240999.480.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.h1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 63520532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '1920.240999.640.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: 63520533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 2, 'counter': 118, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1920.240999.960.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': '960.11357', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11357, '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: 63520534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.960.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: 63520536
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.240999.960.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: 63520537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.240999', 'ambient_counter': 240999, 'ambient_order': 1920, 'ambient_tex': 'C_2^5.A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 1, 'counter': 121, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1920.240999.1920.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': '1920.240999', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2717355043640295321, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1920, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5.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: 63520512
    {'ambient': '1920.240999', '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.a1.a1', '16.a1.a1', '16.a1.a2', '16.a1.a3', '16.a1.a4'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1952, 5000, 819, 5000, 7609, 5000, 788, 5000], 'generators': [85378802302080, 81030234284331171840007, 3425526027544450596486, 206924718200870436600, 206937543839330309160, 347541499243366980819838, 265498044599714152308478], 'label': '1920.240999.1.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': '960.11357', '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': '960.11357'}
  • id: 63520513
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '120.34', 'aut_weyl_index': 64, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['80.b1.a4', '96.a1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [395, -1, 81, -1, 9685, -1, 87, -1], 'generators': [347541499243366980819838, 390201552462805653468233, 81132435459866835843247], 'label': '1920.240999.16.a1.a4', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a4', 'old_label': '16.a1.a4', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a4', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520514
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 960, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.k1.a1', '120.k1.b1', '120.n1.a1'], 'contains': ['480.c1.a1', '480.e1.a1', '480.e1.a2', '480.f2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5784, -1, 6233, -1, 2627, -1, 5676, -1], 'generators': [206924718200870436600, 81132435396718497797167, 78731141971964288083201], 'label': '1920.240999.240.k1.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.k1.a1', 'projective_image': '1920.240999', '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': '4.2'}
  • id: 63520515
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.k2', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.l1.a1', '120.n1.a1'], 'contains': ['480.c2.a1', '480.e1.a1', '480.e1.a2', '480.f1.a1', '480.f2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5190, -1, 5890, -1, 2943, -1, 5467, -1], 'generators': [3425526112872750163206, 206924718200870436600, 81132435396718497797167], 'label': '1920.240999.240.k2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '240.k2.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520516
    {'ambient': '1920.240999', 'aut_centralizer_order': 24, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '80.a2.a1', '80.a2.a2', '80.a3.a1', '80.b1.a1', '80.b1.a2', '80.b1.a3', '80.b1.a4', '160.a1.a1'], 'contains': ['640.a1.a1', '960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [1373, -1, 1423, -1, 8236, -1, 1443, -1], 'generators': [155267940784824464365870, 81132435459866835843247], 'label': '1920.240999.320.a1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.a1.a1', 'old_label': '320.a1.a1', 'projective_image': '960.11357', '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: 63520517
    {'ambient': '1920.240999', 'aut_centralizer_order': 20, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1920, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '192.a1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [340, -1, 659, -1, 625, -1, 485, -1], 'generators': [482085896135896614234286], 'label': '1920.240999.384.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': '1920.240999', '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: 63520518
    {'ambient': '1920.240999', 'aut_centralizer_order': 512, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7680, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.a1.b1', '240.b1.a1', '240.c1.a1', '240.c1.a2', '240.c2.a1', '240.d1.a1', '240.d2.a1', '240.d2.a2', '240.d3.a1'], 'contains': ['960.a1.a1', '960.b1.a1', '960.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5097, -1, 5462, -1, 4619, -1, 4539, -1], 'generators': [3425526027544450596486, 81132435459866835843247], 'label': '1920.240999.480.a1.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': '480.a1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520519
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.c1.a1', '240.c1.a2', '240.c2.a1', '240.e1.a1', '240.e1.a2', '240.e1.a3', '240.e1.a4'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2107, -1, 2348, -1, 6563, -1, 2145, -1], 'generators': [239184344292369459776663, 81132435459866835843247], 'label': '1920.240999.480.b1.a1', 'mobius_quo': None, 'mobius_sub': -64, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '480.b1.a1', 'projective_image': '960.11357', '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: 63520520
    {'ambient': '1920.240999', 'aut_centralizer_order': 256, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '240.f1.a1', '240.f1.b1', '240.g1.a1', '240.g1.a2', '240.h1.a1', '240.i1.a1', '240.i1.a2', '240.k1.a1'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6450, -1, 6630, -1, 2166, -1, 5676, -1], 'generators': [3425526112872750163206, 19583763076649520], 'label': '1920.240999.480.c1.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': '480.c1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520521
    {'ambient': '1920.240999', 'aut_centralizer_order': 128, 'aut_label': '480.c2', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d3.a1', '240.h1.a1', '240.i1.a1', '240.i1.a2', '240.k2.a1'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3875, -1, 4912, -1, 2481, -1, 3912, -1], 'generators': [3425526027544450596486, 206937543839330309160], 'label': '1920.240999.480.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '480.c2.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520522
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.f1.a1', '240.j1.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7675, -1, 8962, -1, 3408, -1, 7204, -1], 'generators': [78884542845972292222201, 242505012243329755712777], 'label': '1920.240999.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.a1', 'old_label': '480.d1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520523
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.b1', '240.f1.b1', '240.j1.b1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7675, -1, 8169, -1, 3408, -1, 8163, -1], 'generators': [3581250984111662633646, 242504993059572424204217], 'label': '1920.240999.480.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.b1', 'old_label': '480.d1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520524
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['40.c1.a1', '60.e1.a1', '80.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8547, -1, 8388, -1, 7294, -1, 8637, -1], 'generators': [206924718200870436600, 155267940784824464365870, 588669340082908328422439, 345905780513593569287176, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.20.a1.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': '20.a1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
  • id: 63520525
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d2.a1', '240.i1.a1', '240.i1.a2', '240.k1.a1', '240.k2.a1'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4209, -1, 4459, -1, 3112, -1, 4121, -1], 'generators': [206937543839330309160, 3581238243788522110206], 'label': '1920.240999.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '480.e1.a1', 'projective_image': '1920.240999', '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: 63520526
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d2.a2', '240.i1.a1', '240.i1.a2', '240.k1.a1', '240.k2.a1'], 'contains': ['960.b1.a1', '960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4209, -1, 5267, -1, 3112, -1, 3703, -1], 'generators': [3581238243788522110206, 19583763076649520], 'label': '1920.240999.480.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '480.e1.a2', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520527
    {'ambient': '1920.240999', 'aut_centralizer_order': 256, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b1.a1', '240.d1.a1', '240.j1.a1', '240.j1.b1', '240.k2.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6153, -1, 7765, -1, 4019, -1, 6906, -1], 'generators': [81030253868094248489527, 3581238243788522110206], 'label': '1920.240999.480.f1.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.f1.a1', 'projective_image': '1920.240999', '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: 63520528
    {'ambient': '1920.240999', 'aut_centralizer_order': 128, 'aut_label': '480.f2', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b2.a1', '240.d3.a1', '240.k1.a1', '240.k2.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4741, -1, 5997, -1, 3704, -1, 4330, -1], 'generators': [81132435396718497797167, 3581238243788522110206], 'label': '1920.240999.480.f2.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': '480.f2.a1', 'projective_image': '1920.240999', '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': '6.1'}
  • id: 63520529
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.g1.a1', '240.g1.a2'], 'contains': ['960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7338, -1, 7403, -1, 1870, -1, 6179, -1], 'generators': [206924718200870436600, 345905780492839024356616], 'label': '1920.240999.480.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '480.g1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520530
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.c1.a1', '240.d2.a1', '240.h1.a1', '240.i1.a1'], 'contains': ['960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2597, -1, 3193, -1, 2796, -1, 3494, -1], 'generators': [206937543839330309160, 3581238158409719808126], 'label': '1920.240999.480.h1.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': '480.h1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520531
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.c1.a2', '240.d2.a2', '240.h1.a1', '240.i1.a2'], 'contains': ['960.c1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2597, -1, 3555, -1, 2796, -1, 3284, -1], 'generators': [78731141886635988516481, 19583763076649520], 'label': '1920.240999.480.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '480.h1.a2', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520532
    {'ambient': '1920.240999', 'aut_centralizer_order': 24, 'aut_label': '640.a1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b1.a1', '160.b2.a1', '160.c1.a1', '160.c1.a2', '320.a1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [1909, -1, 2652, -1, 7221, -1, 2695, -1], 'generators': [155267940784824464365870], 'label': '1920.240999.640.a1.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': '640.a1.a1', 'projective_image': '1920.240999', '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: 63520533
    {'ambient': '1920.240999', 'aut_centralizer_order': 7680, 'aut_label': '960.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7680, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1'], 'contains': ['1920.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1909, 5000, 2348, 5000, 4619, 5000, 2145, 5000], 'generators': [81132435459866835843247], 'label': '1920.240999.960.a1.a1', 'mobius_quo': -1, 'mobius_sub': 3840, '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': '960.11357', 'quotient_action_image': '1.1', 'quotient_action_kernel': '960.11357', 'quotient_action_kernel_order': 960, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520534
    {'ambient': '1920.240999', 'aut_centralizer_order': 512, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7680, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '480.c1.a1', '480.c2.a1', '480.d1.a1', '480.d1.b1', '480.e1.a1', '480.e1.a2', '480.f1.a1', '480.f2.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4948, -1, 5804, -1, 3408, -1, 4435, -1], 'generators': [3581250984111662633646], 'label': '1920.240999.960.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': '960.b1.a1', 'projective_image': '1920.240999', '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: 63520535
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['40.c1.b1', '60.e1.b1', '80.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8547, -1, 9086, -1, 7294, -1, 9394, -1], 'generators': [206924718200870436600, 155267940784824464365870, 81132435459866835843247, 345905761288339363909816, 588413893197173199343919, 78731141971964288083201], 'label': '1920.240999.20.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.b1', 'old_label': '20.a1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
  • id: 63520536
    {'ambient': '1920.240999', 'aut_centralizer_order': 512, 'aut_label': '960.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7680, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '480.c1.a1', '480.c2.a1', '480.e1.a1', '480.e1.a2', '480.g1.a1', '480.h1.a1', '480.h1.a2'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4191, -1, 4912, -1, 2796, -1, 3912, -1], 'generators': [3425526027544450596486], 'label': '1920.240999.960.c1.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': '960.c1.a1', 'projective_image': '1920.240999', '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: 63520537
    {'ambient': '1920.240999', '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': [2107, 5000, 2652, 5000, 3408, 5000, 2695, 5000], 'generators': [], 'label': '1920.240999.1920.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': '1920.240999', '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: 63520538
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 20, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['60.f1.a1', '80.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [4701, -1, 5136, -1, 6575, -1, 4134, -1], 'generators': [206924718200870436600, 155267940784824464365870, 345905780492839024356616, 81132435459866835843247, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '960.11357', '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': '48.3'}
  • id: 63520539
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 20, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['60.g1.a1', '80.a1.a1', '80.b1.a1', '80.b1.a2', '80.b1.a3', '80.b1.a4'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3749, -1, 1923, -1, 8881, -1, 1688, -1], 'generators': [206924718200870436600, 614265903533684470246558, 155267940784824464365870, 345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.20.c1.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': '20.c1.a1', 'projective_image': '960.11357', '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': '48.50'}
  • id: 63520540
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.955', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.a1'], 'contains': ['40.d1.a1', '60.a1.a1', '80.a1.a1', '80.a2.a1', '80.a2.a2', '80.a3.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2861, -1, 3653, -1, 8163, -1, 2856, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 155267940784824464365870, 85378802302080, 81030234284331171840007], 'label': '1920.240999.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63520541
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 24, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['120.m1.a1', '384.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': '24T4945', 'count': 6, 'diagramx': [1488, -1, 1432, -1, 183, -1, 1130, -1], 'generators': [3425526027544450596486, 206924718200870436600, 85378802302080, 81030234284331171840007, 482085896135896614234286], 'label': '1920.240999.24.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': '24.a1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.234'}
  • id: 63520542
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 60, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.b1.a1', '60.b1.b1', '60.d1.a1', '60.g1.a1', '60.i1.a1', '60.i1.b1', '60.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6273, -1, 5952, -1, 4876, -1, 5378, -1], 'generators': [206924718200870436600, 614265903533684470246558, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905761288339363909816], 'label': '1920.240999.30.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': '960.11357', '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': '16.14'}
  • id: 63520543
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 60, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.b1.a1', '60.b1.b1', '60.c1.a1', '60.f1.a1', '60.h1.a1', '60.h1.b1', '60.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7497, -1, 6706, -1, 3596, -1, 6054, -1], 'generators': [206924718200870436600, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905780492839024356616, 614521363224167010799798], 'label': '1920.240999.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520544
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.267', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.b1.b1', '60.c1.a1', '60.d1.a1', '60.e1.b1', '60.h1.b1', '60.i1.b1', '60.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6994, -1, 7382, -1, 4326, -1, 7206, -1], 'generators': [206924718200870436600, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905761288339363909816, 614521363224167010799798], 'label': '1920.240999.30.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': '30.c1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520545
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1536.408633427', 'aut_weyl_index': 5, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['15.a1.a1', '20.a1.a1', '20.a1.b1', '20.b1.a1', '20.c1.a1', '20.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4633, -1, 5136, -1, 7351, -1, 4134, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 155267940784824464365870, 85378802302080, 345905780492839024356616, 81030234284331171840007, 614521363224167010799798], 'label': '1920.240999.5.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': '960.11357', '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': '192.1023'}
  • id: 63520546
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.267', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1', '60.h1.a1', '60.i1.a1', '60.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6994, -1, 7882, -1, 4326, -1, 6508, -1], 'generators': [206924718200870436600, 614265903533684470246558, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905780492839024356616], 'label': '1920.240999.30.c1.b1', '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.c1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520547
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.202', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.h1.a1', '60.h1.b1', '60.i1.a1', '60.i1.b1', '60.j1.a1', '60.k1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5259, -1, 5400, -1, 2908, -1, 4789, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 345905780492839024356616, 81030234284331171840007], 'label': '1920.240999.30.d1.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.d1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520548
    {'ambient': '1920.240999', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '48.48', 'aut_weyl_index': 160, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.a2.a1', '120.c1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1553, -1, 2234, -1, 7674, -1, 2252, -1], 'generators': [3425526112872750163206, 375239517561410066005802, 206924803529170003320, 436508593013325571130137, 81132435459866835843247], 'label': '1920.240999.40.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': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520549
    {'ambient': '1920.240999', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '48.48', 'aut_weyl_index': 160, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.a2.a2', '120.c1.b1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1553, -1, 2763, -1, 7674, -1, 1920, -1], 'generators': [323589007927819998805683, 81132422656408337491327, 78731141886635988516481, 436508593013325571130137, 81132435459866835843247], 'label': '1920.240999.40.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.b1', 'old_label': '40.a1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520550
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '48.48', 'aut_weyl_index': 160, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.a3.a1', '120.e1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2035, -1, 3073, -1, 9343, -1, 2484, -1], 'generators': [323589007927819998805683, 3425526027544450596486, 461236608940818060857502, 81132422571080037924607, 81132435459866835843247], 'label': '1920.240999.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '960.11357', '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': '24.12'}
  • id: 63520551
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1'], 'contains': ['120.j1.a1', '160.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': '40T1654', 'count': 20, 'diagramx': [9866, -1, 9650, -1, 7282, -1, 9190, -1], 'generators': [588413886794774625561119, 81030253931192083800247, 155267940784824464365870, 78884542845972292222201, 345905780513593569287176], 'label': '1920.240999.40.c1.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.c1.a1', 'projective_image': '1920.240999', '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': '48.3'}
  • id: 63520552
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1'], 'contains': ['120.j1.b1', '160.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': '40T1654', 'count': 20, 'diagramx': [9866, -1, 9919, -1, 7282, -1, 9879, -1], 'generators': [81030253931192083800247, 345956852230504965353536, 155267940784824464365870, 78884542845972292222201, 588669346485257166114359], 'label': '1920.240999.40.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.b1', 'old_label': '40.c1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.b1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
  • id: 63520553
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.955', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1'], 'contains': ['120.n1.a1', '160.b1.a1', '160.b2.a1', '160.c1.a1', '160.c1.a2'], 'core': '1920.a1.a1', 'coset_action_label': '40T1579', 'count': 10, 'diagramx': [2763, -1, 3408, -1, 8801, -1, 2940, -1], 'generators': [155267940784824464365870, 85378802302080, 3581238158409719808126, 81030234284331171840007, 19583763076649520], 'label': '1920.240999.40.d1.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': '40.d1.a1', 'projective_image': '1920.240999', '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': '96.227'}
  • id: 63520554
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.34', 'aut_weyl_index': 64, 'centralizer': '60.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.d1.a1', '30.d1.a1'], 'contains': ['120.h1.a1', '120.m1.a1', '120.n1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3394, 5000, 4457, 5000, 705, 5000, 3190, 5000], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 81030234284331171840007], 'label': '1920.240999.60.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': '960.11357', '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': '60.5'}
  • id: 63520555
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.267', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '30.c1.b1'], 'contains': ['120.d1.a1', '120.f1.a1', '120.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7186, -1, 6842, -1, 4326, -1, 6342, -1], 'generators': [206924718200870436600, 345905780513593569287176, 81132435459866835843247, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '960.11357', '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: 63520556
    {'ambient': '1920.240999', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '640.21536', 'aut_weyl_index': 12, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '30.d1.a1', '96.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1507, -1, 1216, -1, 3150, -1, 1130, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 81030234284331171840007, 606346537609438847163670, 482085896135896614234286], 'label': '1920.240999.6.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': '960.11357', '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: 63520557
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.267', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.d1.b1', '120.f1.a1', '120.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7186, -1, 6573, -1, 4326, -1, 6630, -1], 'generators': [206924718200870436600, 345905761309081692848056, 81132435459866835843247, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.60.b1.b1', '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.b1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520558
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.202', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.c1.a1', '30.c1.b1'], 'contains': ['120.a1.a1', '120.d1.a1', '120.d1.b1', '120.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8924, -1, 8072, -1, 3788, -1, 7757, -1], 'generators': [206924718200870436600, 81132435459866835843247, 345905761288339363909816, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.60.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': '960.11357', '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': '16.14'}
  • id: 63520559
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.202', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1', '30.c1.b1'], 'contains': ['120.d1.a1', '120.d1.b1', '120.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6777, -1, 8405, -1, 5487, -1, 7400, -1], 'generators': [206924718200870436600, 345905761309081692848056, 81132435459866835843247, 588413893197173199343919, 78731141971964288083201], 'label': '1920.240999.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '960.11357', '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: 63520560
    {'ambient': '1920.240999', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.49', 'aut_weyl_index': 160, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '30.c1.b1'], 'contains': ['120.d1.a1', '120.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9511, -1, 9550, -1, 6006, -1, 8846, -1], 'generators': [206924718200870436600, 588669340082908328422439, 345905780513593569287176, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.60.e1.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': '60.e1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520561
    {'ambient': '1920.240999', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.49', 'aut_weyl_index': 160, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '30.c1.a1'], 'contains': ['120.d1.b1', '120.j1.b1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9511, -1, 9176, -1, 6006, -1, 9535, -1], 'generators': [206924718200870436600, 81132435459866835843247, 345905761288339363909816, 588413893197173199343919, 78731141971964288083201], 'label': '1920.240999.60.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.e1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520562
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 20, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '30.b1.a1'], 'contains': ['120.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7596, -1, 6304, -1, 3250, -1, 5572, -1], 'generators': [206924718200870436600, 345905780492839024356616, 81132435459866835843247, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.60.f1.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': '60.f1.a1', 'projective_image': '960.11357', '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': '48.50'}
  • id: 63520563
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 20, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '30.a1.a1'], 'contains': ['120.b1.a1', '120.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4241, -1, 3991, -1, 6760, -1, 3496, -1], 'generators': [206924718200870436600, 614265903533684470246558, 345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.60.g1.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': '60.g1.a1', 'projective_image': '960.11357', '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': '48.50'}
  • id: 63520564
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.51', 'aut_weyl_index': 240, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.c1.b1', '30.d1.a1'], 'contains': ['120.d1.a1', '120.f1.a1', '120.h1.a1', '120.i1.a1', '120.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8280, -1, 7648, -1, 1224, -1, 5957, -1], 'generators': [206924718200870436600, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905780492839024356616], 'label': '1920.240999.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.h1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520565
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.51', 'aut_weyl_index': 240, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.c1.a1', '30.d1.a1'], 'contains': ['120.d1.b1', '120.f1.a1', '120.h1.a1', '120.i1.b1', '120.k1.b1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8280, -1, 7201, -1, 1224, -1, 7015, -1], 'generators': [3425526027544450596486, 206924718200870436600, 81030234369709974142087, 206937543839330309160, 345905780492839024356616], 'label': '1920.240999.60.h1.b1', '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.h1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520566
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.51', 'aut_weyl_index': 240, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.b1', '30.d1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.g1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5549, -1, 5944, -1, 4907, -1, 4707, -1], 'generators': [3425526027544450596486, 206924718200870436600, 81030234369709974142087, 206937543839330309160, 345905761309081692848056], 'label': '1920.240999.60.i1.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.i1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520567
    {'ambient': '1920.240999', 'aut_centralizer_order': 2, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 20, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.d1.a1', '30.d1.a1', '40.a1.a1', '40.a1.b1', '40.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2035, -1, 3013, -1, 7809, -1, 2369, -1], 'generators': [323589007927819998805683, 3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 461236608940818060857502, 81030234284331171840007], 'label': '1920.240999.10.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '960.11357', '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': '96.227'}
  • id: 63520568
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.51', 'aut_weyl_index': 240, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1', '30.d1.a1'], 'contains': ['120.c1.b1', '120.d1.b1', '120.g1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5549, -1, 5497, -1, 4907, -1, 5187, -1], 'generators': [206924718200870436600, 81132435396718497797167, 85378802302080, 78731141886635988516481, 345905761288339363909816], 'label': '1920.240999.60.i1.b1', '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.i1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520569
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.202', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.c1.b1', '30.d1.a1'], 'contains': ['120.d1.a1', '120.d1.b1', '120.h1.a1', '120.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4868, -1, 8765, -1, 1947, -1, 8211, -1], 'generators': [3425526112872750163206, 206937606987668355240, 206924718200870436600, 81030234284331171840007, 345905761288339363909816], 'label': '1920.240999.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.j1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520570
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.202', 'aut_weyl_index': 120, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '30.d1.a1'], 'contains': ['120.e1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6230, -1, 5050, -1, 2670, -1, 4228, -1], 'generators': [3425526112872750163206, 206937606987668355240, 206924718200870436600, 345905780492839024356616, 81030234284331171840007], 'label': '1920.240999.60.k1.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.k1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63520571
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.a1.b1', '20.b1.a1', '20.c1.a1', '20.d1.a1'], 'contains': ['160.b1.a1', '240.d1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [4042, -1, 4671, -1, 8189, -1, 5641, -1], 'generators': [206924718200870436600, 155267940784824464365870, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.80.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': '80.a1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520572
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '80.a2', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '40.a1.a1'], 'contains': ['160.c1.a1', '240.d2.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1547, -1, 2278, -1, 7521, -1, 2315, -1], 'generators': [81132435396718497797167, 155267940784824464365870, 85378802302080, 81132422571080037924607], 'label': '1920.240999.80.a2.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.a2.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520573
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '80.a2', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '40.a1.b1'], 'contains': ['160.c1.a2', '240.d2.a2', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1547, -1, 2777, -1, 7521, -1, 1971, -1], 'generators': [206937606987668355240, 155267940784824464365870, 3581238158409719808126, 81030234284331171840007], 'label': '1920.240999.80.a2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.b1', 'old_label': '80.a2.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a2.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520574
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '80.a3', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '40.b1.a1'], 'contains': ['160.b2.a1', '240.d3.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2035, -1, 3099, -1, 9150, -1, 2660, -1], 'generators': [81030234369709974142087, 206937543839330309160, 155267940784824464365870, 78731141886635988516481], 'label': '1920.240999.80.a3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.a3.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a3.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520575
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 320, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '20.c1.a1'], 'contains': ['240.e1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [869, -1, 1628, -1, 9869, -1, 1688, -1], 'generators': [239133253350191642340623, 155267940784824464365870, 613141909208280568303912, 81132435459866835843247], 'label': '1920.240999.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.b1.a1', 'old_label': '80.b1.a1', 'projective_image': '960.11357', '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: 63520576
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 320, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a2', '20.c1.a1'], 'contains': ['240.e1.a2', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [869, -1, 1128, -1, 9869, -1, 959, -1], 'generators': [155267940784824464365870, 242504993038817879273657, 613397362496364535074352, 81132435459866835843247], 'label': '1920.240999.80.b1.a2', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.b1.a2', 'old_label': '80.b1.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520577
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 320, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a3', '20.c1.a1'], 'contains': ['240.e1.a3', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [869, -1, 1923, -1, 9869, -1, 1178, -1], 'generators': [155267940784824464365870, 614521356821768437016998, 239184344292369459776663, 81132435459866835843247], 'label': '1920.240999.80.b1.a3', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.b1.a3', 'old_label': '80.b1.a3', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a3', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520578
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 24, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.a1.a1', '60.a1.a1', '192.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1488, -1, 1316, -1, 590, -1, 1130, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 81030234284331171840007, 482085896135896614234286], 'label': '1920.240999.12.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': '960.11357', '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: 63520579
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 320, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a4', '20.c1.a1'], 'contains': ['240.e1.a4', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [869, -1, 1423, -1, 9869, -1, 643, -1], 'generators': [614265903533684470246558, 155267940784824464365870, 242556083980995696709697, 81132435459866835843247], 'label': '1920.240999.80.b1.a4', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.b1.a4', 'old_label': '80.b1.a4', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a4', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520580
    {'ambient': '1920.240999', 'aut_centralizer_order': 2, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '40.12', 'aut_weyl_index': 192, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '16.a1.a1', '16.a1.a2', '16.a1.a3', '16.a1.a4'], 'contains': ['192.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [134, -1, 438, -1, 6406, -1, 125, -1], 'generators': [612170539370337640635784, 81132435459866835843247, 482085896135896614234286], 'label': '1920.240999.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '960.11357', '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: 63520581
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1'], 'contains': ['240.a1.a1', '240.a1.b1', '240.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8305, -1, 8198, -1, 4576, -1, 7885, -1], 'generators': [81132435459866835843247, 345905761288339363909816, 614521363224167010799798, 78731141971964288083201], 'label': '1920.240999.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '120.a1.a1', 'projective_image': '960.11357', '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': '4.2'}
  • id: 63520582
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '32.27', 'aut_weyl_index': 240, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.a1'], 'contains': ['240.c1.a1', '240.c1.a2', '240.c2.a1', '240.e1.a1', '240.e1.a2', '240.e1.a3', '240.e1.a4'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4654, -1, 2908, -1, 6848, -1, 3203, -1], 'generators': [614265903533684470246558, 345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '120.b1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520583
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '8.5', 'aut_weyl_index': 960, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '60.i1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.d2.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3183, -1, 3936, -1, 6010, -1, 4616, -1], 'generators': [3425526027544450596486, 81132422656408337491327, 345905761309081692848056, 81132435459866835843247], 'label': '1920.240999.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '120.c1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520584
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '8.5', 'aut_weyl_index': 960, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '60.i1.b1'], 'contains': ['240.a1.b1', '240.c1.a2', '240.d2.a2'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3183, -1, 4410, -1, 6010, -1, 4327, -1], 'generators': [206924803529170003320, 345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.b1', 'old_label': '120.c1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520585
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 960, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1', '60.h1.a1', '60.i1.a1', '60.j1.a1'], 'contains': ['240.a1.a1', '240.d1.a1', '240.f1.a1', '240.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7139, -1, 8870, -1, 3781, -1, 7566, -1], 'generators': [206924718200870436600, 345905780513593569287176, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520586
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.5', 'aut_weyl_index': 960, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.b1', '60.c1.a1', '60.d1.a1', '60.e1.b1', '60.h1.b1', '60.i1.b1', '60.j1.a1'], 'contains': ['240.a1.b1', '240.d1.a1', '240.f1.b1', '240.j1.b1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7139, -1, 8495, -1, 3781, -1, 8204, -1], 'generators': [206924718200870436600, 81132435459866835843247, 345905761288339363909816, 78731141971964288083201], 'label': '1920.240999.120.d1.b1', '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.d1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520587
    {'ambient': '1920.240999', 'aut_centralizer_order': 16, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.5', 'aut_weyl_index': 960, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '60.k1.a1'], 'contains': ['240.b1.a1', '240.c2.a1', '240.d3.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3894, -1, 4678, -1, 4972, -1, 4039, -1], 'generators': [3425526112872750163206, 206924718200870436600, 345905780492839024356616, 81132435459866835843247], 'label': '1920.240999.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.k1.a1', 'old_label': '120.e1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520588
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 480, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.b1.b1', '60.c1.a1', '60.f1.a1', '60.h1.a1', '60.h1.b1', '60.k1.a1'], 'contains': ['240.b1.a1', '240.d1.a1', '240.g1.a1', '240.g1.a2'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7708, -1, 6825, -1, 3177, -1, 6589, -1], 'generators': [206924718200870436600, 345905780492839024356616, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.120.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': '960.11357', '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': '8.5'}
  • id: 63520589
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 20, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1', '30.c1.b1', '30.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6820, -1, 6233, -1, 4326, -1, 5763, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080, 345905780492839024356616, 81030234284331171840007, 614521363224167010799798], 'label': '1920.240999.15.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': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 63520590
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 480, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.b1.b1', '60.d1.a1', '60.g1.a1', '60.i1.a1', '60.i1.b1', '60.k1.a1'], 'contains': ['240.c1.a1', '240.c1.a2', '240.c2.a1', '240.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5784, -1, 5311, -1, 5491, -1, 5268, -1], 'generators': [206924718200870436600, 345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.120.g1.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.g1.a1', 'projective_image': '960.11357', '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': '8.5'}
  • id: 63520591
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 960, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.h1.a1', '60.h1.b1', '60.i1.a1', '60.i1.b1', '60.j1.a1', '60.k1.a1'], 'contains': ['240.d1.a1', '240.d2.a1', '240.d2.a2', '240.d3.a1', '240.h1.a1', '240.i1.a1', '240.i1.a2', '240.k1.a1', '240.k2.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5212, -1, 5664, -1, 2281, -1, 4866, -1], 'generators': [3425526027544450596486, 206924718200870436600, 81132435396718497797167, 85378802302080], 'label': '1920.240999.120.h1.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': '120.h1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520592
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.h1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8678, -1, 7685, -1, 1155, -1, 5957, -1], 'generators': [206924718200870436600, 85378802302080, 78731141886635988516481, 345905780492839024356616], 'label': '1920.240999.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '120.i1.a1', 'projective_image': '1920.240999', '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': '8.5'}
  • id: 63520593
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.b1'], 'contains': ['240.f1.b1', '240.g1.a2', '240.h1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8678, -1, 7146, -1, 1155, -1, 6934, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 345905780492839024356616], 'label': '1920.240999.120.i1.b1', '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.i1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63520594
    {'ambient': '1920.240999', 'aut_centralizer_order': 16, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.5', 'aut_weyl_index': 640, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '60.e1.a1'], 'contains': ['240.j1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9511, -1, 9783, -1, 4242, -1, 8895, -1], 'generators': [81030253931192083800247, 588669340082908328422439, 78884542845972292222201, 345956871455759170730896], 'label': '1920.240999.120.j1.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': '120.j1.a1', 'projective_image': '1920.240999', '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': '3.1'}
  • id: 63520595
    {'ambient': '1920.240999', 'aut_centralizer_order': 16, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.5', 'aut_weyl_index': 640, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.b1', '60.e1.b1'], 'contains': ['240.j1.b1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9511, -1, 9564, -1, 4242, -1, 9535, -1], 'generators': [81030253931192083800247, 345956852230504965353536, 78884542845972292222201, 588669346485257166114359], 'label': '1920.240999.120.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.b1', 'old_label': '120.j1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63520596
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.k1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9087, -1, 7954, -1, 1589, -1, 6245, -1], 'generators': [206924718200870436600, 81132435396718497797167, 345905780492839024356616, 78731141971964288083201], 'label': '1920.240999.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '120.k1.a1', 'projective_image': '1920.240999', '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': '8.5'}
  • id: 63520597
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.14', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.b1'], 'contains': ['240.f1.b1', '240.g1.a2', '240.k1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9087, -1, 7415, -1, 1589, -1, 7222, -1], 'generators': [206924718200870436600, 81030234369709974142087, 3581250984111662633646, 345905780492839024356616], 'label': '1920.240999.120.k1.b1', '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.k1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63520598
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 480, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1'], 'contains': ['240.j1.a1', '240.j1.b1', '240.k2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6273, -1, 9331, -1, 2658, -1, 8548, -1], 'generators': [3425526112872750163206, 206937606987668355240, 342585112541878728420502, 81132422571080037924607], 'label': '1920.240999.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.j1.a1', 'old_label': '120.l1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520599
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 384, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.a1.a1'], 'contains': ['240.h1.a1', '240.i1.a1', '240.i1.a2'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2829, -1, 3261, -1, 740, -1, 3580, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160, 85378802302080], 'label': '1920.240999.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '120.m1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63520600
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '120.34', 'aut_weyl_index': 64, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['80.b1.a1', '96.a1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [395, -1, 736, -1, 9685, -1, 842, -1], 'generators': [248636368969660808403833, 390201552462805653468233, 81132435459866835843247], 'label': '1920.240999.16.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': '960.11357', '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: 63520601
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 640, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '60.a1.a1'], 'contains': ['240.i1.a1', '240.i1.a2', '240.k1.a1', '240.k2.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3538, -1, 4174, -1, 1966, -1, 3789, -1], 'generators': [3425526027544450596486, 206937543839330309160, 85378802302080, 81132422571080037924607], 'label': '1920.240999.120.n1.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': '120.n1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520602
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '12.4', 'aut_weyl_index': 640, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.a2', '16.a1.a3', '16.a1.a4', '40.a1.a1', '40.a1.b1', '40.b1.a1'], 'contains': ['320.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [822, -1, 890, -1, 8236, -1, 1181, -1], 'generators': [81132435459866835843247, 435384592285535628473503, 370794970548950745167292], 'label': '1920.240999.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '960.11357', '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': '6.1'}
  • id: 63520603
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '40.c1.b1', '40.d1.a1', '80.a1.a1'], 'contains': ['480.f1.a1', '640.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [4462, -1, 7961, -1, 7221, -1, 8163, -1], 'generators': [81030253868094248489527, 155267940784824464365870, 3581238243788522110206], 'label': '1920.240999.160.b1.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.b1.a1', 'projective_image': '1920.240999', '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': '12.3'}
  • id: 63520604
    {'ambient': '1920.240999', 'aut_centralizer_order': 8, 'aut_label': '160.b2', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '80.a3.a1'], 'contains': ['480.f2.a1', '640.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2137, -1, 3715, -1, 7920, -1, 2879, -1], 'generators': [81030234369709974142087, 155267940784824464365870, 78884555586295432745641], 'label': '1920.240999.160.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '160.b2.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520605
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '80.a2.a1'], 'contains': ['480.h1.a1', '640.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1717, -1, 2106, -1, 6944, -1, 2695, -1], 'generators': [155267940784824464365870, 85378802302080, 19583763076649520], 'label': '1920.240999.160.c1.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.c1.a1', 'projective_image': '1920.240999', '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': '24.12'}
  • id: 63520606
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '80.a2.a2'], 'contains': ['480.h1.a2', '640.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1717, -1, 2549, -1, 6944, -1, 2512, -1], 'generators': [155267940784824464365870, 3581238158409719808126, 81030234284331171840007], 'label': '1920.240999.160.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.b1', 'old_label': '160.c1.a2', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63520607
    {'ambient': '1920.240999', 'aut_centralizer_order': 20, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1920, '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': [160, -1, 528, -1, 625, -1, 176, -1], 'generators': [81132435459866835843247, 482085896135896614234286], 'label': '1920.240999.192.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': '960.11357', '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: 63520608
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.c1.a1', '120.d1.a1'], 'contains': ['480.a1.a1', '480.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6845, -1, 8988, -1, 5353, -1, 7551, -1], 'generators': [342585093358121396911942, 78884542845972292222201, 81132435459866835843247], 'label': '1920.240999.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '240.a1.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520609
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.c1.b1', '120.d1.b1'], 'contains': ['480.a1.a1', '480.d1.b1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6845, -1, 8342, -1, 5353, -1, 7898, -1], 'generators': [81132435459866835843247, 345905761288339363909816, 78731141971964288083201], 'label': '1920.240999.240.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.a1.b1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520610
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.e1.a1', '120.f1.a1'], 'contains': ['480.a1.a1', '480.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7338, -1, 6559, -1, 3884, -1, 5954, -1], 'generators': [206924718200870436600, 345905780492839024356616, 81132435459866835843247], 'label': '1920.240999.240.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': '240.b1.a1', 'projective_image': '960.11357', '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': '4.2'}
  • id: 63520611
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '120.34', 'aut_weyl_index': 64, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['80.b1.a2', '96.a1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [395, -1, 291, -1, 9685, -1, 622, -1], 'generators': [248636369032502984271353, 390201552462805653468233, 81132435459866835843247], 'label': '1920.240999.16.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a2', 'old_label': '16.a1.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a2', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520612
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '120.c1.a1', '120.g1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4303, -1, 3620, -1, 6398, -1, 4883, -1], 'generators': [78884542845972292222201, 345905761309081692848056, 81132435459866835843247], 'label': '1920.240999.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '960.11357', '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: 63520613
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '120.c1.b1', '120.g1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4303, -1, 4139, -1, 6398, -1, 4536, -1], 'generators': [345905761309081692848056, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.240.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.c1.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520614
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.c2', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '120.e1.a1', '120.g1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4795, -1, 4853, -1, 5875, -1, 4190, -1], 'generators': [206924718200870436600, 345905761309081692848056, 81132435459866835843247], 'label': '1920.240999.240.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.c2.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c2.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520615
    {'ambient': '1920.240999', 'aut_centralizer_order': 256, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '120.d1.a1', '120.d1.b1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.c1.a1', '480.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6450, -1, 6825, -1, 4303, -1, 6232, -1], 'generators': [206924718200870436600, 81132435459866835843247, 78731141971964288083201], 'label': '1920.240999.240.d1.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': '240.d1.a1', 'projective_image': '960.11357', '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': '3.1'}
  • id: 63520616
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.d2', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a2.a1', '120.c1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.e1.a1', '480.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2785, -1, 3360, -1, 4619, -1, 3703, -1], 'generators': [206924718200870436600, 78731141886635988516481, 81132435459866835843247], 'label': '1920.240999.240.d2.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': '240.d2.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520617
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.d2', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a2.a2', '120.c1.b1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.e1.a2', '480.h1.a2'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2785, -1, 4593, -1, 4619, -1, 3075, -1], 'generators': [3425526027544450596486, 206924718200870436600, 81132435459866835843247], 'label': '1920.240999.240.d2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '240.d2.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d2.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520618
    {'ambient': '1920.240999', 'aut_centralizer_order': 128, 'aut_label': '240.d3', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1280, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a3.a1', '120.e1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.c2.a1', '480.f2.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3745, -1, 5214, -1, 4934, -1, 3912, -1], 'generators': [3425526112872750163206, 206924718200870436600, 81132435459866835843247], 'label': '1920.240999.240.d3.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': '240.d3.a1', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d3.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63520619
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '120.b1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2122, -1, 2348, -1, 7498, -1, 2328, -1], 'generators': [614265903533684470246558, 239184344292369459776663, 81132435459866835843247], 'label': '1920.240999.240.e1.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': '240.e1.a1', 'projective_image': '960.11357', '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': '12.3'}
  • id: 63520620
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a2', '120.b1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2122, -1, 2006, -1, 7498, -1, 1961, -1], 'generators': [239184344292369459776663, 613141909208280568303912, 81132435459866835843247], 'label': '1920.240999.240.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '240.e1.a2', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520621
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a3', '120.b1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2122, -1, 2520, -1, 7498, -1, 2145, -1], 'generators': [614521356821768437016998, 239184344292369459776663, 81132435459866835843247], 'label': '1920.240999.240.e1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '240.e1.a3', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a3', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520622
    {'ambient': '1920.240999', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '120.34', 'aut_weyl_index': 64, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['80.b1.a3', '96.a1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [395, -1, 1064, -1, 9685, -1, 403, -1], 'generators': [347541499306209156687358, 390201552462805653468233, 81132435459866835843247], 'label': '1920.240999.16.a1.a3', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a3', 'old_label': '16.a1.a3', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a3', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520623
    {'ambient': '1920.240999', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '24.12', 'aut_weyl_index': 320, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a4', '120.b1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2122, -1, 2177, -1, 7498, -1, 1777, -1], 'generators': [239184344292369459776663, 613397362496364535074352, 81132435459866835843247], 'label': '1920.240999.240.e1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '240.e1.a4', 'projective_image': '960.11357', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a4', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520624
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.i1.a1', '120.k1.a1'], 'contains': ['480.c1.a1', '480.d1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8816, -1, 8664, -1, 2208, -1, 6857, -1], 'generators': [206924718200870436600, 345905780513593569287176, 78731141971964288083201], 'label': '1920.240999.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '240.f1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520625
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '120.i1.b1', '120.k1.b1'], 'contains': ['480.c1.a1', '480.d1.b1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8816, -1, 7512, -1, 2208, -1, 8428, -1], 'generators': [206924718200870436600, 3581250984111662633646, 242504993059572424204217], 'label': '1920.240999.240.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.f1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520626
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.a1', '120.i1.a1', '120.k1.a1'], 'contains': ['480.c1.a1', '480.g1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8323, -1, 8018, -1, 1055, -1, 6510, -1], 'generators': [206924718200870436600, 345905780492839024356616, 78731141971964288083201], 'label': '1920.240999.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '240.g1.a1', 'projective_image': '1920.240999', '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: 63520627
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.a1', '120.i1.b1', '120.k1.b1'], 'contains': ['480.c1.a1', '480.g1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8323, -1, 7085, -1, 1055, -1, 7204, -1], 'generators': [206924718200870436600, 3581250984111662633646, 345905780492839024356616], 'label': '1920.240999.240.g1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.g1.a2', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520628
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 960, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.i1.a1', '120.i1.b1', '120.m1.a1'], 'contains': ['480.c1.a1', '480.c2.a1', '480.h1.a1', '480.h1.a2'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5487, -1, 5423, -1, 1474, -1, 5258, -1], 'generators': [3425526027544450596486, 206924718200870436600, 206937543839330309160], 'label': '1920.240999.240.h1.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.h1.a1', 'projective_image': '1920.240999', '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': '4.2'}
  • id: 63520629
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.m1.a1', '120.n1.a1'], 'contains': ['480.c1.a1', '480.c2.a1', '480.e1.a1', '480.e1.a2', '480.h1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3285, -1, 4398, -1, 1789, -1, 3494, -1], 'generators': [206937606987668355240, 206924718200870436600, 78731141886635988516481], 'label': '1920.240999.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '240.i1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520630
    {'ambient': '1920.240999', 'aut_centralizer_order': 64, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3840, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.m1.a1', '120.n1.a1'], 'contains': ['480.c1.a1', '480.c2.a1', '480.e1.a1', '480.e1.a2', '480.h1.a2'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3285, -1, 3879, -1, 1789, -1, 3284, -1], 'generators': [3425526112872750163206, 206924718200870436600, 206937543839330309160], 'label': '1920.240999.240.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '240.i1.a2', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520631
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.j1.a1', '120.l1.a1'], 'contains': ['480.d1.a1', '480.f1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7831, -1, 9636, -1, 3362, -1, 8775, -1], 'generators': [81030253931192083800247, 78884542845972292222201, 345956871455759170730896], 'label': '1920.240999.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.b1', 'old_label': '240.j1.a1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520632
    {'ambient': '1920.240999', 'aut_centralizer_order': 32, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1920, 'centralizer': '60.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '120.j1.b1', '120.l1.a1'], 'contains': ['480.d1.b1', '480.f1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7831, -1, 9312, -1, 3362, -1, 9122, -1], 'generators': [81030253931192083800247, 345956852230504965353536, 78884542845972292222201], 'label': '1920.240999.240.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.j1.b1', 'projective_image': '1920.240999', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}