Abstract group data - 240.124

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 4, 60], 'aut_gens': [[1, 4, 8], [1, 4, 88], [1, 4, 12], [1, 4, 188], [57, 4, 12]], 'aut_group': '960.11038', 'aut_hash': 11038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 12, 'aut_perms': [720, 87091200, 127371618, 87464231], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 5, 2, 1], [2, 10, 1, 1], [3, 2, 1, 1], [4, 30, 2, 2], [5, 4, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 10, 2, 2], [10, 4, 1, 1], [10, 4, 2, 1], [15, 4, 2, 1], [30, 4, 2, 1], [30, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3\\times D_4\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '240.195', 'autcentquo_hash': 195, 'autcentquo_nilpotent': False, 'autcentquo_order': 240, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 5, 2], [2, 10, 1], [3, 2, 1], [4, 30, 4], [5, 4, 1], [6, 2, 3], [6, 10, 4], [10, 4, 3], [15, 4, 2], [30, 4, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '120.41', 'commutator_count': 1, 'commutator_label': '30.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 124, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 5, 1, 2], [2, 10, 1, 1], [3, 2, 1, 1], [4, 30, 2, 2], [5, 4, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 10, 1, 2], [6, 10, 2, 1], [10, 4, 1, 1], [10, 4, 2, 1], [15, 4, 2, 1], [30, 4, 2, 1], [30, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 60, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '120.41', 'hash': 124, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [4, 1, 30], 'inner_gens': [[1, 4, 140], [1, 4, 8], [117, 4, 8]], 'inner_hash': 41, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': False, 'inner_tex': 'C_{30}:C_4', 'inner_used': [1, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 12]], 'label': '240.124', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 20, 'linQ_dim': 8, 'linQ_dim_count': 12, 'linR_count': 4, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D10.D6', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 30, 'number_divisions': 20, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 68, 'number_subgroups': 320, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 120], [5, 4], [6, 46], [10, 12], [15, 8], [30, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[121, 4, 8], [1, 4, 12], [1, 4, 88]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 4], [8, 3], [16, 1]], 'representations': {'PC': {'code': 142030415629314272430516703239, 'gens': [1, 3, 4], 'pres': [6, -2, -2, -2, 2, -3, -5, 12, 3363, 1833, 69, 964, 970, 118, 3461, 3467]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [12211, 24181, 92201, 8081, 72001, 130311]}, 'Perm': {'d': 12, 'gens': [40280409, 7620480, 16, 87091200, 5760, 46]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}.D_6', 'transitive_degree': 60, '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: 109359012
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 124, 'group_order': 240, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109359023
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 124, 'group_order': 240, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 4, 'size': 1}
  • id: 109359034
    {'aut_label': '2B', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 124, 'group_order': 240, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 120, 'size': 2}
  • id: 109359036
    {'aut_label': '2C', 'centralizer': '5.a1.a1', 'counter': 4, 'group_counter': 124, 'group_order': 240, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 98, 'size': 5}
  • id: 109359037
    {'aut_label': '2C', 'centralizer': '5.a1.a1', 'counter': 5, 'group_counter': 124, 'group_order': 240, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 102, 'size': 5}
  • id: 109359038
    {'aut_label': '2E', 'centralizer': '10.a1.a1', 'counter': 6, 'group_counter': 124, 'group_order': 240, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 170, 'size': 10}
  • id: 109359039
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 124, 'group_order': 240, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 80, 'size': 2}
  • id: 109359040
    {'aut_label': '4A1', 'centralizer': '30.b1.a1', 'counter': 8, 'group_counter': 124, 'group_order': 240, 'label': '4A1', 'order': 4, 'powers': [4, 9, 8], 'representative': 179, 'size': 30}
  • id: 109359041
    {'aut_label': '4A-1', 'centralizer': '30.b1.a1', 'counter': 9, 'group_counter': 124, 'group_order': 240, 'label': '4A-1', 'order': 4, 'powers': [4, 8, 9], 'representative': 129, 'size': 30}
  • id: 109359013
    {'aut_label': '4A-1', 'centralizer': '30.b1.b1', 'counter': 10, 'group_counter': 124, 'group_order': 240, 'label': '4B1', 'order': 4, 'powers': [5, 11, 10], 'representative': 137, 'size': 30}
  • id: 109359014
    {'aut_label': '4A1', 'centralizer': '30.b1.b1', 'counter': 11, 'group_counter': 124, 'group_order': 240, 'label': '4B-1', 'order': 4, 'powers': [5, 10, 11], 'representative': 239, 'size': 30}
  • id: 109359015
    {'aut_label': '5A', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 124, 'group_order': 240, 'label': '5A', 'order': 5, 'powers': [12, 12, 1], 'representative': 96, 'size': 4}
  • id: 109359016
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 124, 'group_order': 240, 'label': '6A', 'order': 6, 'powers': [7, 2, 13], 'representative': 84, 'size': 2}
  • id: 109359017
    {'aut_label': '6B1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 124, 'group_order': 240, 'label': '6B1', 'order': 6, 'powers': [7, 3, 15], 'representative': 40, 'size': 2}
  • id: 109359018
    {'aut_label': '6B1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 124, 'group_order': 240, 'label': '6B-1', 'order': 6, 'powers': [7, 3, 14], 'representative': 200, 'size': 2}
  • id: 109359019
    {'aut_label': '6C', 'centralizer': '10.a1.a1', 'counter': 16, 'group_counter': 124, 'group_order': 240, 'label': '6C', 'order': 6, 'powers': [7, 4, 16], 'representative': 18, 'size': 10}
  • id: 109359020
    {'aut_label': '6C', 'centralizer': '10.a1.a1', 'counter': 17, 'group_counter': 124, 'group_order': 240, 'label': '6D', 'order': 6, 'powers': [7, 5, 17], 'representative': 22, 'size': 10}
  • id: 109359021
    {'aut_label': '6E1', 'centralizer': '10.a1.a1', 'counter': 18, 'group_counter': 124, 'group_order': 240, 'label': '6E1', 'order': 6, 'powers': [7, 6, 19], 'representative': 10, 'size': 10}
  • id: 109359022
    {'aut_label': '6E1', 'centralizer': '10.a1.a1', 'counter': 19, 'group_counter': 124, 'group_order': 240, 'label': '6E-1', 'order': 6, 'powers': [7, 6, 18], 'representative': 14, 'size': 10}
  • id: 109359024
    {'aut_label': '10A', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 124, 'group_order': 240, 'label': '10A', 'order': 10, 'powers': [12, 20, 2], 'representative': 52, 'size': 4}
  • id: 109359025
    {'aut_label': '10B1', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 124, 'group_order': 240, 'label': '10B1', 'order': 10, 'powers': [12, 22, 3], 'representative': 24, 'size': 4}
  • id: 109359026
    {'aut_label': '10B1', 'centralizer': '4.a1.a1', 'counter': 22, 'group_counter': 124, 'group_order': 240, 'label': '10B3', 'order': 10, 'powers': [12, 21, 3], 'representative': 72, 'size': 4}
  • id: 109359027
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 124, 'group_order': 240, 'label': '15A1', 'order': 15, 'powers': [23, 12, 7], 'representative': 32, 'size': 4}
  • id: 109359028
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 124, 'group_order': 240, 'label': '15A-1', 'order': 15, 'powers': [24, 12, 7], 'representative': 208, 'size': 4}
  • id: 109359029
    {'aut_label': '30A1', 'centralizer': '4.a1.a1', 'counter': 25, 'group_counter': 124, 'group_order': 240, 'label': '30A1', 'order': 30, 'powers': [23, 20, 13], 'representative': 20, 'size': 4}
  • id: 109359030
    {'aut_label': '30A1', 'centralizer': '4.a1.a1', 'counter': 26, 'group_counter': 124, 'group_order': 240, 'label': '30A-1', 'order': 30, 'powers': [24, 20, 13], 'representative': 116, 'size': 4}
  • id: 109359031
    {'aut_label': '30B1', 'centralizer': '4.a1.a1', 'counter': 27, 'group_counter': 124, 'group_order': 240, 'label': '30B1', 'order': 30, 'powers': [23, 21, 14], 'representative': 8, 'size': 4}
  • id: 109359032
    {'aut_label': '30B1', 'centralizer': '4.a1.a1', 'counter': 28, 'group_counter': 124, 'group_order': 240, 'label': '30B-1', 'order': 30, 'powers': [24, 21, 15], 'representative': 60, 'size': 4}
  • id: 109359033
    {'aut_label': '30B1', 'centralizer': '4.a1.a1', 'counter': 29, 'group_counter': 124, 'group_order': 240, 'label': '30B7', 'order': 30, 'powers': [24, 22, 14], 'representative': 56, 'size': 4}
  • id: 109359035
    {'aut_label': '30B1', 'centralizer': '4.a1.a1', 'counter': 30, 'group_counter': 124, 'group_order': 240, 'label': '30B-7', 'order': 30, 'powers': [23, 22, 15], 'representative': 12, 'size': 4}
• 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: 4238815
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4238826
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 4238828
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 4238829
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4238830
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2], 'schur_index': 1}
  • id: 4238831
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4238832
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4238833
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 2, 0, 0, -2, 2, 2, 0, -2, 0, 0, -2, 0], 'schur_index': 1}
  • id: 4238834
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 2, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, -2, 0, 0, -2, 2, 2, 0, -2, 0, 0, -2, 0], 'schur_index': 1}
  • id: 4238816
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, -1, 0, 0, 0, 0, 2, 1, -1, 1, 1, 1, -1, -1, -2, -2, 2, -1, -1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 4238817
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2e', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -1, 0, 0, 0, 0, 2, 1, -1, 1, -1, -1, 1, 1, -2, -2, 2, -1, -1, 1, -1, 1, 1, -1, 1], 'schur_index': 2}
  • id: 4238818
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2f', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, -1, 0, 0, 0, 0, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 2}
  • id: 4238819
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2g', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, -4, 4, 0, -2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, -2, 0, 0, -4, -2, -2, 0, 2, 0, 0, 2, 0], 'schur_index': 1}
  • id: 4238820
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.2h', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -4, 0, -2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 2, 0, 0, -4, -2, -2, 0, 2, 0, 0, 2, 0], 'schur_index': 1}
  • id: 4238821
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, -1, 4, 4, 4, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4238822
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4b', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 4, 0, 0, 0, 0, -1, -4, 4, -4, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 4238823
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4c', 'multiplicity': 2, 'nt': [15, 6], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, 0, -4, 0, 0, 0, 0, -2, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4238824
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4d', 'multiplicity': 2, 'nt': [20, 19], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, 0, 2, 0], 'schur_index': 1}
  • id: 4238825
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4e', 'multiplicity': 2, 'nt': [30, 17], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, -4, 0, 0, 0, 0, -2, 4, -4, 4, 0, 0, 0, 0, 2, 2, -2, 1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 4238827
    {'cdim': 4, 'counter': 20, 'faithful': True, 'group': '240.124', 'group_order': 240, 'image': None, 'label': '240.124.4f', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, -2, 0, 0, -2, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 6266709
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 240, 'label': '240.124.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6266720
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 120, 'label': '240.124.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 6266731
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 120, 'label': '240.124.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 6266733
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 120, 'label': '240.124.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6266734
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 60, 'label': '240.124.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 6266735
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 60, 'label': '240.124.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 6266736
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 60, 'label': '240.124.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 6266737
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 240, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 60, 'label': '240.124.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 6266738
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 40, 'label': '240.124.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6266710
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 60, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 30, 'label': '240.124.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 6266711
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 60, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 30, 'label': '240.124.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 6266712
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 20, 'label': '240.124.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6266713
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.a1', 'kernel_order': 20, 'label': '240.124.2e', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6266714
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 40, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 20, 'label': '240.124.2f', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6266715
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 20, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 10, 'label': '240.124.2g1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]]]}
  • id: 6266716
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 20, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 10, 'label': '240.124.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 6266717
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 20, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 10, 'label': '240.124.2h1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]]]}
  • id: 6266718
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 20, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 10, 'label': '240.124.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 6266719
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 12, 'counter': 19, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 12, 'label': '240.124.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6266721
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 12, 'counter': 20, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.a1', 'kernel_order': 6, 'label': '240.124.4b', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6266722
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 15, 'dim': 4, 'faithful': False, 'field': [4, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '60.7', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.124.4c1', 'nt': [15, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]]]}
  • id: 6266723
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 15, 'dim': 4, 'faithful': False, 'field': [4, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '60.7', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 4, 'label': '240.124.4c2', 'nt': [15, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]]]}
  • id: 6266724
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 6, 'counter': 23, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '80.34', 'image_order': 80, 'indicator': 1, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.124.4d1', 'nt': [20, 19], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 2], [2, -2]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0], [2, 2], [2, -2]], [[1, 0]], [[1, 0], [2, 2], [2, -2]]]}
  • id: 6266725
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 6, 'counter': 24, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '80.34', 'image_order': 80, 'indicator': 1, 'kernel': '80.a1.a1', 'kernel_order': 3, 'label': '240.124.4d2', 'nt': [20, 19], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0], [2, 2], [2, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 2], [2, -2]], [[1, 0]], [[1, 0], [2, 2], [2, -2]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0]], [[-1, 0], [-2, 2], [-2, -2]]]}
  • id: 6266726
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 15, 'dim': 4, 'faithful': False, 'field': [4, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '120.41', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.124.4e1', 'nt': [30, 17], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]]]}
  • id: 6266727
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 15, 'dim': 4, 'faithful': False, 'field': [4, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '120.41', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 2, 'label': '240.124.4e2', 'nt': [30, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]]]}
  • id: 6266728
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 15, 'dim': 4, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '240.124', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.124.4f1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0], [-4, 5]], [[2, 0]], [[2, 0], [4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [2, 2], [-2, 3], [2, 7]], [[1, 0], [-2, 2], [2, 3], [-2, 7]], [[1, 0]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [1, 2], [-1, 3], [-1, 5], [1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[1, 2], [-1, 3], [1, 5], [1, 7]], [[1, 0], [-1, 2], [1, 3], [1, 5], [-1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 2], [1, 3], [-1, 5], [-1, 7]]]}
  • id: 6266729
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 15, 'dim': 4, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '240.124', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.124.4f2', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0], [4, 5]], [[2, 0]], [[-2, 0], [-4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [2, 2], [-2, 3], [2, 7]], [[1, 0], [-2, 2], [2, 3], [-2, 7]], [[1, 0]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[1, 2], [-1, 3], [1, 5], [1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [1, 2], [-1, 3], [-1, 5], [1, 7]], [[-1, 2], [1, 3], [-1, 5], [-1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[1, 0], [-1, 2], [1, 3], [1, 5], [-1, 7]]]}
  • id: 6266730
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 15, 'dim': 4, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '240.124', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.124.4f3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0], [-4, 5]], [[2, 0]], [[2, 0], [4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-2, 2], [2, 3], [-2, 7]], [[-1, 0], [2, 2], [-2, 3], [2, 7]], [[1, 0]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 2], [1, 3], [-1, 5], [-1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 0], [-1, 2], [1, 3], [1, 5], [-1, 7]], [[1, 2], [-1, 3], [1, 5], [1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [1, 2], [-1, 3], [-1, 5], [1, 7]]]}
  • id: 6266732
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 15, 'dim': 4, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '240.124', 'group_counter': 124, 'group_order': 240, 'image': None, 'image_isoclass': '240.124', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 1, 'label': '240.124.4f4', 'nt': [60, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0], [4, 5]], [[2, 0]], [[-2, 0], [-4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-2, 2], [2, 3], [-2, 7]], [[-1, 0], [2, 2], [-2, 3], [2, 7]], [[1, 0]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 0], [-1, 2], [1, 3], [1, 5], [-1, 7]], [[1, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 2], [1, 3], [-1, 5], [-1, 7]], [[-1, 0], [1, 2], [-1, 3], [-1, 5], [1, 7]], [[-2, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[1, 2], [-1, 3], [1, 5], [1, 7]]]}
• 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: 64209215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 240, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '240.124.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.124', 'subgroup_hash': 124, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 120, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.44', 'subgroup_hash': 44, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 40, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '240.124.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 60, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64209280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 60, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 60, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209217
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209218
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '240.124.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 40, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209223
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 30, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.124.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64209224
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209225
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209227
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 64209228
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 20, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 20, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 20, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209238
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209239
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '240.124.15.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 2}
  • id: 64209241
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 15, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '240.124.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 64209242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 12, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209245
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209246
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209247
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209249
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.20.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209250
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 10, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.124.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209251
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209252
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209253
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64209254
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 5, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 64209255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.30.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64209256
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209258
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 6, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.124.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209260
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209261
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209262
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.40.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209263
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 64209264
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 5, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '240.124.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.19', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 19, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_4', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 64209265
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '240.124.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64209266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64209267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64209268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64209269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '240.124.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64209271
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209272
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.60.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64209273
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 3, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '240.124.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}:C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 64209274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '240.124.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.41', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}:C_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 64209275
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64209276
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64209277
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64209278
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '240.124.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64209279
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '240.124', 'ambient_counter': 124, 'ambient_order': 240, 'ambient_tex': 'D_{10}.D_6', 'central': True, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '240.124.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '240.124', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 124, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}.D_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C6'], '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: 64209260
    {'ambient': '240.124', 'aut_centralizer_order': 240, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.a1.a1', '20.d1.a1', '20.d1.b1'], 'contains': ['80.a1.a1', '120.b1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5357, -1, 3928, -1, 1797, -1, 1739, -1], 'generators': [120, 160], 'label': '240.124.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209215
    {'ambient': '240.124', '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': '120.a1.a1', 'complements': ['240.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2314, 4566, 8123, 4436, 6998, 2400, 7287, 3009], 'generators': [1, 48, 2, 4, 120, 160], 'label': '240.124.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '120.41', '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': '120.41'}
  • id: 64209216
    {'ambient': '240.124', 'aut_centralizer_order': 6, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.d1.a1', '12.d1.b1', '20.d1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5951, -1, 3369, -1, 4057, -1, 3466, -1], 'generators': [150, 160, 48, 120], 'label': '240.124.4.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 64209217
    {'ambient': '240.124', 'aut_centralizer_order': 2, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 8, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '12.e1.a1', '20.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1821, -1, 8846, -1, 9537, -1, 9691, -1], 'generators': [1, 160, 48, 2], 'label': '240.124.4.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.e1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
  • id: 64209218
    {'ambient': '240.124', 'aut_centralizer_order': 2, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 8, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.b1.b1', '12.e1.b1', '20.e1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1821, -1, 7211, -1, 9537, -1, 6399, -1], 'generators': [57, 160, 48, 54], 'label': '240.124.4.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '4.e1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
  • id: 64209219
    {'ambient': '240.124', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.38', 'aut_weyl_index': 20, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '15.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [407, -1, 9829, -1, 7282, -1, 7287, -1], 'generators': [1, 160, 120, 2, 4], 'label': '240.124.5.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': '120.41', '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': '12.4'}
  • id: 64209220
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.50', 'aut_weyl_index': 12, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5186, 7223, 4180, 7636, 4883, 3171, 5267, 4152], 'generators': [2, 120, 48, 4], 'label': '240.124.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '120.41', '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': '20.3'}
  • id: 64209221
    {'ambient': '240.124', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '30.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2303, -1, 8392, -1, 7974, -1, 9230, -1], 'generators': [1, 2, 48, 4], 'label': '240.124.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 64209222
    {'ambient': '240.124', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.b1', '30.b1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2303, -1, 7660, -1, 7974, -1, 7540, -1], 'generators': [57, 54, 48, 4], 'label': '240.124.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 64209261
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.b1.a1', '20.d1.a1', '20.e1.a1'], 'contains': ['80.a1.a1', '120.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2702, -1, 5541, -1, 6786, -1, 6249, -1], 'generators': [2, 160], 'label': '240.124.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '240.124', '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': '2.1'}
  • id: 64209223
    {'ambient': '240.124', 'aut_centralizer_order': 120, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 120, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9593, 4077, 898, 5150, 2360, 5214, 1723, 5927], 'generators': [4, 48, 160], 'label': '240.124.8.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209224
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '40.c1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4005, 1076, 5697, 2807, 6736, 1057, 6949, 723], 'generators': [2, 48, 160], 'label': '240.124.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209225
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.b1', '4.e1.b1'], 'contains': ['16.a1.a1', '24.b1.b1', '40.c1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4005, 1076, 5122, 850, 6736, 1057, 5833, 2389], 'generators': [150, 48, 160], 'label': '240.124.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209226
    {'ambient': '240.124', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.236', 'aut_weyl_index': 6, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1', '6.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5186, 6265, 4727, 7135, 4883, 3757, 4367, 5307], 'generators': [2, 120, 160, 4, 48], 'label': '240.124.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209227
    {'ambient': '240.124', 'aut_centralizer_order': 60, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 120, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '24.c1.a1', '40.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7592, -1, 1848, -1, 195, -1, 697, -1], 'generators': [120, 48, 160], 'label': '240.124.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209228
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '24.d1.a1', '40.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8966, -1, 1372, -1, 2991, -1, 2737, -1], 'generators': [218, 48, 160], 'label': '240.124.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 64209229
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '8.5', 'aut_weyl_index': 120, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1', '20.d1.b1', '30.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3207, -1, 6816, -1, 5764, -1, 4065, -1], 'generators': [2, 4, 120, 160], 'label': '240.124.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209230
    {'ambient': '240.124', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.e1.a1', '30.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [413, -1, 9826, -1, 8817, -1, 8615, -1], 'generators': [1, 4, 2, 160], 'label': '240.124.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 64209231
    {'ambient': '240.124', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.e1.b1', '30.b1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [413, -1, 8296, -1, 8817, -1, 6925, -1], 'generators': [57, 4, 54, 160], 'label': '240.124.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 64209232
    {'ambient': '240.124', 'aut_centralizer_order': 120, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 120, 'centralizer': '4.a1.a1', 'complements': ['20.e1.a1', '20.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6894, 8200, 2226, 8379, 898, 7014, 1210, 7459], 'generators': [4, 48, 120], 'label': '240.124.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209233
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1', '60.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4637, 2920, 5900, 4208, 7366, 2671, 7409, 3763], 'generators': [2, 48, 4], 'label': '240.124.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209234
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': ['20.e1.a1', '20.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '60.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8190, 5922, 149, 6579, 3622, 3943, 3198, 4845], 'generators': [218, 48, 4], 'label': '240.124.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209235
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.d1.a1', '60.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5612, -1, 4130, -1, 4883, -1, 5373, -1], 'generators': [2, 48, 120], 'label': '240.124.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 64209236
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.a1.a1'], 'contains': ['24.b1.b1', '24.c1.a1', '24.d1.a1', '60.d1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5612, -1, 3432, -1, 4883, -1, 4672, -1], 'generators': [150, 48, 120], 'label': '240.124.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 64209237
    {'ambient': '240.124', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '240.195', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['120.b1.a1', '120.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '6.b1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2031, 2848, 8552, 4436, 8002, 1057, 8615, 3009], 'generators': [1, 2, 160, 4, 48], 'label': '240.124.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '120.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.41'}
  • id: 64209238
    {'ambient': '240.124', 'aut_centralizer_order': 4, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '60.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1927, -1, 8821, -1, 9336, -1, 9890, -1], 'generators': [1, 48, 2], 'label': '240.124.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209239
    {'ambient': '240.124', 'aut_centralizer_order': 4, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.b1.b1'], 'contains': ['24.b1.b1', '60.e1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1927, -1, 7472, -1, 9336, -1, 8114, -1], 'generators': [57, 48, 54], 'label': '240.124.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.e1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209240
    {'ambient': '240.124', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.b1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [557, -1, 9851, -1, 7282, -1, 8045, -1], 'generators': [1, 120], 'label': '240.124.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '120.41', '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': '4.2'}
  • id: 64209241
    {'ambient': '240.124', 'aut_centralizer_order': 120, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 120, 'centralizer': '4.a1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1'], 'contains': ['48.a1.a1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9521, 1546, 1267, 2050, 2701, 3657, 3051, 2839], 'generators': [160, 48], 'label': '240.124.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['48.a1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '240.124', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209242
    {'ambient': '240.124', 'aut_centralizer_order': 240, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '2.a1.a1', 'complements': ['12.e1.a1', '12.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '60.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5585, 7712, 3482, 9150, 1735, 9157, 240, 9282], 'generators': [4, 120, 160], 'label': '240.124.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209243
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['40.a1.a1', '40.c1.a1', '40.c1.b1', '60.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2182, -1, 7593, -1, 7997, -1, 6391, -1], 'generators': [2, 4, 160], 'label': '240.124.20.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209244
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.d1.a1', '60.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6760, -1, 2911, -1, 4252, -1, 2179, -1], 'generators': [218, 4, 160], 'label': '240.124.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209245
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.a1.a1'], 'contains': ['40.b1.a1', '40.c1.a1', '40.d1.a1', '60.d1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4620, -1, 5584, -1, 5513, -1, 4212, -1], 'generators': [2, 120, 160], 'label': '240.124.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209246
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '10.a1.a1'], 'contains': ['40.b1.a1', '40.c1.b1', '40.d1.a1', '60.d1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4620, -1, 4853, -1, 5513, -1, 3658, -1], 'generators': [150, 120, 160], 'label': '240.124.20.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.d1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64209247
    {'ambient': '240.124', 'aut_centralizer_order': 8, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 160, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.b1.a1'], 'contains': ['40.c1.a1', '60.e1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1339, -1, 9098, -1, 9793, -1, 9556, -1], 'generators': [1, 2, 160], 'label': '240.124.20.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.e1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 64209248
    {'ambient': '240.124', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '240.195', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['120.b1.a1', '120.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.b1', '6.b1.b1', '10.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2031, 2848, 7652, 2064, 8002, 1057, 6762, 991], 'generators': [57, 54, 160, 4, 48], 'label': '240.124.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '120.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '120.41'}
  • id: 64209249
    {'ambient': '240.124', 'aut_centralizer_order': 8, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 160, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '10.b1.b1'], 'contains': ['40.c1.b1', '60.e1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1339, -1, 8232, -1, 9793, -1, 7780, -1], 'generators': [57, 54, 160], 'label': '240.124.20.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '20.e1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 64209250
    {'ambient': '240.124', 'aut_centralizer_order': 240, 'aut_label': '24.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8218, 4548, 326, 5236, 3192, 4914, 3409, 4881], 'generators': [4, 48], 'label': '240.124.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209251
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '120.c1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3717, 2196, 6500, 3950, 6384, 2514, 6900, 1866], 'generators': [2, 48], 'label': '240.124.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209252
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.b1.a1', '12.d1.b1', '12.e1.b1'], 'contains': ['48.a1.a1', '120.c1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3717, 2196, 4121, 2378, 6384, 2514, 5857, 3811], 'generators': [150, 48], 'label': '240.124.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.b1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209253
    {'ambient': '240.124', 'aut_centralizer_order': 120, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['48.a1.a1', '120.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7609, -1, 2091, -1, 1350, -1, 2692, -1], 'generators': [120, 48], 'label': '240.124.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209254
    {'ambient': '240.124', 'aut_centralizer_order': 24, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['48.a1.a1', '120.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9138, -1, 696, -1, 4040, -1, 4363, -1], 'generators': [218, 48], 'label': '240.124.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 64209255
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.c1.a1', '60.d1.a1', '60.d1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3789, -1, 7160, -1, 6122, -1, 5022, -1], 'generators': [2, 4, 120], 'label': '240.124.30.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209256
    {'ambient': '240.124', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [796, -1, 9670, -1, 8756, -1, 9092, -1], 'generators': [1, 4], 'label': '240.124.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209257
    {'ambient': '240.124', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '30.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.e1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [796, -1, 8598, -1, 8756, -1, 8538, -1], 'generators': [57, 4], 'label': '240.124.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.b1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209258
    {'ambient': '240.124', 'aut_centralizer_order': 480, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6461, 6121, 3045, 6879, 3638, 6057, 2367, 5903], 'generators': [4, 160], 'label': '240.124.40.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.4', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209259
    {'ambient': '240.124', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 6, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2597, -1, 8127, -1, 6713, -1, 7703, -1], 'generators': [1, 2, 4, 120, 48], 'label': '240.124.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 64209262
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '20.b1.a1', '20.d1.b1', '20.e1.b1'], 'contains': ['80.a1.a1', '120.c1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2702, -1, 5845, -1, 6786, -1, 5564, -1], 'generators': [150, 160], 'label': '240.124.40.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.c1.b1', 'projective_image': '240.124', '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': '2.1'}
  • id: 64209263
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.c1.a1', '20.d1.a1', '20.d1.b1'], 'contains': ['80.a1.a1', '120.d1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6954, -1, 3566, -1, 4442, -1, 3735, -1], 'generators': [218, 160], 'label': '240.124.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209264
    {'ambient': '240.124', 'aut_centralizer_order': 240, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '4.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.c1.a1', '24.d1.a1'], 'contains': ['240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8401, 2196, 1074, 2807, 3203, 3829, 4069, 3811], 'generators': [48], 'label': '240.124.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '240.124', 'quotient_action_image': '4.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209265
    {'ambient': '240.124', 'aut_centralizer_order': 480, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '2.a1.a1', 'complements': ['4.e1.a1', '4.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5385, 7712, 3049, 7907, 2227, 7157, 2053, 7459], 'generators': [4, 120], 'label': '240.124.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '30.2', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209266
    {'ambient': '240.124', 'aut_centralizer_order': 96, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1', '30.b1.a1', '30.b1.b1'], 'contains': ['120.a1.a1', '120.c1.a1', '120.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3417, -1, 7664, -1, 7316, -1, 6562, -1], 'generators': [2, 4], 'label': '240.124.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '120.41', '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': '1.1'}
  • id: 64209267
    {'ambient': '240.124', 'aut_centralizer_order': 96, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7541, -1, 2128, -1, 4872, -1, 4049, -1], 'generators': [218, 4], 'label': '240.124.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '120.41', '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': '2.1'}
  • id: 64209268
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.d1.a1', '30.a1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4631, -1, 5311, -1, 5452, -1, 5018, -1], 'generators': [2, 120], 'label': '240.124.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209269
    {'ambient': '240.124', 'aut_centralizer_order': 48, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '20.d1.b1', '30.a1.a1'], 'contains': ['120.b1.a1', '120.c1.b1', '120.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4631, -1, 4512, -1, 5452, -1, 4676, -1], 'generators': [150, 120], 'label': '240.124.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '60.d1.b1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64209270
    {'ambient': '240.124', 'aut_centralizer_order': 60, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 60, 'centralizer': '4.a1.a1', 'complements': ['60.e1.a1', '60.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7243, 8924, 2272, 8964, 1735, 7429, 1210, 7775], 'generators': [4, 160, 48, 120], 'label': '240.124.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64209271
    {'ambient': '240.124', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.e1.a1', '30.b1.a1'], 'contains': ['120.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1488, -1, 9224, -1, 9046, -1, 9324, -1], 'generators': [1], 'label': '240.124.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.e1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209272
    {'ambient': '240.124', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '30.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '20.e1.b1', '30.b1.b1'], 'contains': ['120.c1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1488, -1, 8056, -1, 9046, -1, 7947, -1], 'generators': [57], 'label': '240.124.60.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '60.e1.b1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209273
    {'ambient': '240.124', 'aut_centralizer_order': 480, 'aut_label': '80.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1', '40.c1.b1', '40.d1.a1'], 'contains': ['240.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6062, 3770, 3630, 4679, 3627, 4943, 3483, 4893], 'generators': [160], 'label': '240.124.80.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.124', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.13', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64209274
    {'ambient': '240.124', 'aut_centralizer_order': 960, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1'], 'contains': ['240.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6472, 5579, 2595, 5979, 4029, 6014, 3776, 5866], 'generators': [4], 'label': '240.124.120.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.41', 'quotient_action_image': '1.1', 'quotient_action_kernel': '120.41', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64209275
    {'ambient': '240.124', 'aut_centralizer_order': 480, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.b1.a1', '60.a1.a1', '60.d1.a1', '60.d1.b1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5335, -1, 4050, -1, 2227, -1, 2941, -1], 'generators': [120], 'label': '240.124.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209276
    {'ambient': '240.124', 'aut_centralizer_order': 96, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.c1.a1', '60.b1.a1', '60.d1.a1', '60.e1.a1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3667, -1, 7165, -1, 6585, -1, 6403, -1], 'generators': [2], 'label': '240.124.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209277
    {'ambient': '240.124', 'aut_centralizer_order': 96, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '40.c1.b1', '60.b1.a1', '60.d1.b1', '60.e1.b1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3667, -1, 5811, -1, 6585, -1, 5711, -1], 'generators': [150], 'label': '240.124.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.c1.b1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209278
    {'ambient': '240.124', 'aut_centralizer_order': 96, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.d1.a1', '60.c1.a1', '60.d1.a1', '60.d1.b1'], 'contains': ['240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6998, -1, 3348, -1, 4442, -1, 4363, -1], 'generators': [218], 'label': '240.124.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209279
    {'ambient': '240.124', 'aut_centralizer_order': None, 'aut_label': '240.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': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.c1.a1', '120.c1.b1', '120.d1.a1'], 'contains': [], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6323, 3770, 3630, 4679, 3828, 4943, 4069, 4893], 'generators': [], 'label': '240.124.240.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.124', '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': '1.1'}
  • id: 64209280
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '80.50', 'aut_weyl_index': 12, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.b1.a1', '20.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4260, 2848, 5593, 4065, 6585, 1057, 5935, 2353], 'generators': [2, 160, 48, 4], 'label': '240.124.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '120.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209281
    {'ambient': '240.124', 'aut_centralizer_order': 12, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.50', 'aut_weyl_index': 12, 'centralizer': '20.a1.a1', 'complements': ['60.e1.a1', '60.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '12.c1.a1', '20.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8966, 5452, 952, 6235, 3292, 5286, 2737, 5951], 'generators': [218, 160, 48, 4], 'label': '240.124.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '120.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 64209282
    {'ambient': '240.124', 'aut_centralizer_order': 6, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '12.d1.a1', '20.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5951, -1, 4281, -1, 4057, -1, 4664, -1], 'generators': [2, 160, 48, 120], 'label': '240.124.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '240.124', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}