Abstract group data - 144.41

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 36, 'aut_gen_orders': [2, 2, 6, 36], 'aut_gens': [[1, 2, 4], [73, 2, 4], [1, 2, 68], [1, 2, 28], [57, 38, 4]], 'aut_group': '864.2583', 'aut_hash': 2583, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 864, 'aut_permdeg': 15, 'aut_perms': [127, 39492673920, 44228620806, 556800174408], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 9, 2, 1], [2, 18, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 2, 1, 1], [6, 4, 2, 1], [9, 2, 3, 1], [12, 4, 1, 1], [18, 2, 3, 1], [18, 4, 6, 1], [36, 4, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_{36}:C_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '108.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 108, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{18}:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 9, 2], [2, 18, 2], [3, 2, 1], [4, 2, 1], [4, 18, 1], [6, 2, 1], [6, 4, 2], [9, 2, 3], [12, 4, 1], [18, 2, 3], [18, 4, 6], [36, 4, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '72.17', 'commutator_count': 1, 'commutator_label': '18.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 41, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 2, 1, 1], [6, 4, 1, 2], [9, 2, 3, 1], [12, 4, 1, 1], [18, 2, 3, 1], [18, 4, 3, 2], [36, 4, 3, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1008, 'exponent': 36, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 1, 3]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '24.14', 'hash': 41, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 2, 18], 'inner_gens': [[1, 2, 68], [1, 2, 76], [81, 74, 4]], 'inner_hash': 17, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_2\\times D_{18}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 18], [4, 4]], 'label': '144.41', 'linC_count': 27, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 27, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D4*D9', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 15, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 30, 'number_divisions': 20, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 51, 'number_subgroup_classes': 81, 'number_subgroups': 355, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 59], [3, 2], [4, 20], [6, 10], [9, 6], [12, 4], [18, 30], [36, 12]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [108, 0], 'outer_gens': [[1, 38, 4], [73, 2, 20]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [720, 28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1], [6, 4], [12, 1]], 'representations': {'PC': {'code': 1120729382158378463262467, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -3, 1226, 692, 50, 3267, 69, 3844, 118, 3461]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 1089247, 1318384, 385262, 70633, 638353]}, 'Perm': {'d': 13, 'gens': [94434600, 5, 7, 16, 609725520, 1133733000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4\\times D_9', 'transitive_degree': 36, '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: 108763002
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 41, 'group_order': 144, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 108763013
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 41, 'group_order': 144, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 72, 'size': 1}
  • id: 108763024
    {'aut_label': '2B', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 41, 'group_order': 144, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2, 'size': 2}
  • id: 108763026
    {'aut_label': '2B', 'centralizer': '2.a1.b1', 'counter': 4, 'group_counter': 41, 'group_order': 144, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 38, 'size': 2}
  • id: 108763027
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 5, 'group_counter': 41, 'group_order': 144, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 9}
  • id: 108763028
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 6, 'group_counter': 41, 'group_order': 144, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 9, 'size': 9}
  • id: 108763029
    {'aut_label': '2F', 'centralizer': '18.b1.a1', 'counter': 7, 'group_counter': 41, 'group_order': 144, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 139, 'size': 18}
  • id: 108763030
    {'aut_label': '2F', 'centralizer': '18.b1.b1', 'counter': 8, 'group_counter': 41, 'group_order': 144, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 79, 'size': 18}
  • id: 108763031
    {'aut_label': '3A', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 41, 'group_order': 144, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 96, 'size': 2}
  • id: 108763003
    {'aut_label': '4A', 'centralizer': '2.d1.a1', 'counter': 10, 'group_counter': 41, 'group_order': 144, 'label': '4A', 'order': 4, 'powers': [2, 10], 'representative': 36, 'size': 2}
  • id: 108763004
    {'aut_label': '4B', 'centralizer': '18.d1.a1', 'counter': 11, 'group_counter': 41, 'group_order': 144, 'label': '4B', 'order': 4, 'powers': [2, 11], 'representative': 61, 'size': 18}
  • id: 108763005
    {'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 41, 'group_order': 144, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 24, 'size': 2}
  • id: 108763006
    {'aut_label': '6B', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 41, 'group_order': 144, 'label': '6B', 'order': 6, 'powers': [9, 3], 'representative': 50, 'size': 4}
  • id: 108763007
    {'aut_label': '6B', 'centralizer': '4.a1.b1', 'counter': 14, 'group_counter': 41, 'group_order': 144, 'label': '6C', 'order': 6, 'powers': [9, 4], 'representative': 86, 'size': 4}
  • id: 108763008
    {'aut_label': '9A1', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 41, 'group_order': 144, 'label': '9A1', 'order': 9, 'powers': [16, 9], 'representative': 32, 'size': 2}
  • id: 108763009
    {'aut_label': '9A1', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 41, 'group_order': 144, 'label': '9A2', 'order': 9, 'powers': [17, 9], 'representative': 64, 'size': 2}
  • id: 108763010
    {'aut_label': '9A1', 'centralizer': '2.c1.a1', 'counter': 17, 'group_counter': 41, 'group_order': 144, 'label': '9A4', 'order': 9, 'powers': [15, 9], 'representative': 128, 'size': 2}
  • id: 108763011
    {'aut_label': '12A', 'centralizer': '4.d1.a1', 'counter': 18, 'group_counter': 41, 'group_order': 144, 'label': '12A', 'order': 12, 'powers': [12, 10], 'representative': 12, 'size': 4}
  • id: 108763012
    {'aut_label': '18A1', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 41, 'group_order': 144, 'label': '18A1', 'order': 18, 'powers': [17, 12], 'representative': 8, 'size': 2}
  • id: 108763014
    {'aut_label': '18A1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 41, 'group_order': 144, 'label': '18A5', 'order': 18, 'powers': [16, 12], 'representative': 40, 'size': 2}
  • id: 108763015
    {'aut_label': '18A1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 41, 'group_order': 144, 'label': '18A7', 'order': 18, 'powers': [15, 12], 'representative': 56, 'size': 2}
  • id: 108763016
    {'aut_label': '18B1', 'centralizer': '4.a1.a1', 'counter': 22, 'group_counter': 41, 'group_order': 144, 'label': '18B1', 'order': 18, 'powers': [15, 13], 'representative': 18, 'size': 4}
  • id: 108763017
    {'aut_label': '18B1', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 41, 'group_order': 144, 'label': '18B5', 'order': 18, 'powers': [17, 13], 'representative': 10, 'size': 4}
  • id: 108763018
    {'aut_label': '18B1', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 41, 'group_order': 144, 'label': '18B7', 'order': 18, 'powers': [16, 13], 'representative': 34, 'size': 4}
  • id: 108763019
    {'aut_label': '18B1', 'centralizer': '4.a1.b1', 'counter': 25, 'group_counter': 41, 'group_order': 144, 'label': '18C1', 'order': 18, 'powers': [16, 14], 'representative': 6, 'size': 4}
  • id: 108763020
    {'aut_label': '18B1', 'centralizer': '4.a1.b1', 'counter': 26, 'group_counter': 41, 'group_order': 144, 'label': '18C5', 'order': 18, 'powers': [15, 14], 'representative': 54, 'size': 4}
  • id: 108763021
    {'aut_label': '18B1', 'centralizer': '4.a1.b1', 'counter': 27, 'group_counter': 41, 'group_order': 144, 'label': '18C7', 'order': 18, 'powers': [17, 14], 'representative': 102, 'size': 4}
  • id: 108763022
    {'aut_label': '36A1', 'centralizer': '4.d1.a1', 'counter': 28, 'group_counter': 41, 'group_order': 144, 'label': '36A1', 'order': 36, 'powers': [19, 18], 'representative': 4, 'size': 4}
  • id: 108763023
    {'aut_label': '36A1', 'centralizer': '4.d1.a1', 'counter': 29, 'group_counter': 41, 'group_order': 144, 'label': '36A5', 'order': 36, 'powers': [20, 18], 'representative': 52, 'size': 4}
  • id: 108763025
    {'aut_label': '36A1', 'centralizer': '4.d1.a1', 'counter': 30, 'group_counter': 41, 'group_order': 144, 'label': '36A7', 'order': 36, 'powers': [21, 18], 'representative': 100, '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: 3998662
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1a', '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: 3998673
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1b', '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: 3998675
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1c', '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: 3998676
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1d', '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: 3998677
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1e', '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: 3998678
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1f', '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: 3998679
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1g', '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: 3998680
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.1h', '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: 3998681
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3998663
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, -2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 2, 2, 2, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998664
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 2, 2, 2, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998665
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 0, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3998666
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, -2, 2, -1, -1, -1, -2, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3998667
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, 2, 2, -2, -1, -1, -1, -2, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3998672
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, -2, -2, -2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998668
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2g', 'multiplicity': 3, 'nt': [9, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -3, 6, 0, -3, -3, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998669
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2h', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, -3, 6, 0, -3, 3, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998670
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2i', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 0, 0, 0, 0, -3, -6, 0, -3, 3, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998671
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.2j', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 0, 0, 0, 0, -3, -6, 0, -3, -3, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3998674
    {'cdim': 4, 'counter': 20, 'faithful': True, 'group': '144.41', 'group_order': 144, 'image': None, 'label': '144.41.4b', 'multiplicity': 3, 'nt': [36, 135], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5670699
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 144, 'label': '144.41.1a', '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: 5670710
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 72, 'label': '144.41.1b', '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: 5670721
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 72, 'label': '144.41.1c', '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: 5670723
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 72, 'label': '144.41.1d', '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: 5670724
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 72, 'label': '144.41.1e', '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: 5670725
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 72, 'label': '144.41.1f', '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: 5670726
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 72, 'label': '144.41.1g', '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: 5670727
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 72, 'label': '144.41.1h', '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: 5670728
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 24, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 24, 'label': '144.41.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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: 5670700
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 36, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 18, 'label': '144.41.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5670701
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 36, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 18, 'label': '144.41.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5670702
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 24, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 12, 'label': '144.41.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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: 5670703
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 24, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 12, 'label': '144.41.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 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: 5670704
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 24, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 12, 'label': '144.41.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 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: 5670705
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 15, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 8, 'label': '144.41.2g1', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
  • id: 5670706
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 8, 'label': '144.41.2g2', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 5670707
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 8, 'label': '144.41.2g3', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 5670708
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 4, 'label': '144.41.2h1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
  • id: 5670709
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 4, 'label': '144.41.2h2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 5670711
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 4, 'label': '144.41.2h3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 5670712
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.b1', 'kernel_order': 4, 'label': '144.41.2i1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]]]}
  • id: 5670713
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.b1', 'kernel_order': 4, 'label': '144.41.2i2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 5670714
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 23, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.b1', 'kernel_order': 4, 'label': '144.41.2i3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 5670715
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 4, 'label': '144.41.2j1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]]]}
  • id: 5670716
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 25, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 4, 'label': '144.41.2j2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 5670717
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 8, 'counter': 26, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 4, 'label': '144.41.2j3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 5670718
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 6, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 3, 'label': '144.41.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5670719
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '144.41', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 1, 'label': '144.41.4b1', 'nt': [36, 135], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5670720
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '144.41', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 1, 'label': '144.41.4b2', 'nt': [36, 135], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5670722
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '144.41', 'group_counter': 41, 'group_order': 144, 'image': None, 'image_isoclass': '144.41', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 1, 'label': '144.41.4b3', 'nt': [36, 135], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 61887179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 144, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '144.41.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.41', 'subgroup_hash': 41, 'subgroup_order': 144, 'subgroup_tex': 'D_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.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': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.8', 'subgroup_hash': 8, 'subgroup_order': 72, 'subgroup_tex': 'C_9:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.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': '72.8', 'subgroup_hash': 8, 'subgroup_order': 72, 'subgroup_tex': 'C_9:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 72, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 72, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 72, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.6', 'subgroup_hash': 6, 'subgroup_order': 72, 'subgroup_tex': 'D_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 61887259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.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': '4.2', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 36, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.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': '4.2', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887185
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 61887186
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 36, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.4.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.c1', 'outer_equivalence': False, 'perfect': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.4.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.d1', 'outer_equivalence': False, 'perfect': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61887199
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887200
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.41.8.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887202
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 30, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.41.8.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887203
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.8.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887204
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61887205
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.8.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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887206
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61887207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '144.41.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 61887208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.12.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': '12.4', '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887210
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 12, 'counter': 38, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61887211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887215
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.c1', 'outer_equivalence': False, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.12.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.d1', 'outer_equivalence': False, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887220
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '144.41.16.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': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 3}
  • id: 61887221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.41.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_9', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61887224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61887225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887229
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 6, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.24.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': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S'], '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: 61887230
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887231
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61887232
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887233
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887235
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.24.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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887236
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 61887238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.41.36.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 61887239
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 4, 'counter': 64, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887240
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61887244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887246
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887248
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.41.36.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61887249
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 3, 'counter': 73, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.48.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': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 61887250
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 2, 'counter': 74, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '144.41.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.17', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{18}', 'simple': True, 'solvable': True, 'special_labels': ['Z', '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: 61887251
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 61887252
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, '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: 61887253
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 61887254
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, '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: 61887255
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 61887257
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.41.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, '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: 61887258
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.41', 'ambient_counter': 41, 'ambient_order': 144, 'ambient_tex': 'D_4\\times D_9', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '144.41.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '144.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_9', '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: 61887179
    {'ambient': '144.41', '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': '72.a1.a1', 'complements': ['144.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5874, 5172, 6311, 5017, 4903, 4809, 4539, 4720], 'generators': [1, 48, 16, 2, 36, 72], 'label': '144.41.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '72.17', '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': '72.17'}
  • id: 61887180
    {'ambient': '144.41', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 72, 'centralizer': '4.a1.a1', 'complements': ['36.f1.c1', '36.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2222, 6035, 5393, 7470, 2536, 5689, 4049, 6140], 'generators': [2, 72, 112, 48], 'label': '144.41.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887181
    {'ambient': '144.41', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 72, 'centralizer': '4.a1.b1', 'complements': ['36.f1.a1', '36.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.b1', '12.a1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2222, 6035, 3643, 2565, 2536, 5689, 2021, 7829], 'generators': [38, 72, 112, 48], 'label': '144.41.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887182
    {'ambient': '144.41', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '108.26', 'aut_weyl_index': 8, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3744, 2328, 2746, 1141, 930, 1242, 2615, 1114], 'generators': [1, 72, 16, 48], 'label': '144.41.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '72.17', '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': '18.1'}
  • id: 61887183
    {'ambient': '144.41', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 8, 'centralizer': '36.a1.a1', 'complements': ['36.f1.c1', '36.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '12.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3114, 3862, 4704, 3989, 1595, 3870, 3035, 4834], 'generators': [3, 72, 16, 48], 'label': '144.41.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887184
    {'ambient': '144.41', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 8, 'centralizer': '36.a1.b1', 'complements': ['36.f1.a1', '36.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.b1', '12.d1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3114, 3862, 4333, 4995, 1595, 3870, 3455, 2036], 'generators': [55, 72, 16, 48], 'label': '144.41.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887185
    {'ambient': '144.41', 'aut_centralizer_order': 72, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 72, 'centralizer': '4.d1.a1', 'complements': ['36.f1.a1', '36.f1.b1', '36.f1.c1', '36.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5958, 8206, 7255, 8894, 5329, 7509, 6114, 3912], 'generators': [36, 112, 72, 48], 'label': '144.41.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887186
    {'ambient': '144.41', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '108.26', 'aut_weyl_index': 8, 'centralizer': '36.b1.a1', 'complements': ['36.f1.a1', '36.f1.b1', '36.f1.c1', '36.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '12.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4699, 759, 5926, 6023, 4657, 2556, 6539, 2979], 'generators': [53, 72, 16, 48], 'label': '144.41.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887187
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '12.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1324, -1, 3118, -1, 265, -1, 1007, -1], 'generators': [1, 2, 16, 48], 'label': '144.41.4.f1.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.f1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887188
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.d1.a1', '12.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1324, -1, 2209, -1, 265, -1, 1427, -1], 'generators': [73, 2, 16, 48], 'label': '144.41.4.f1.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.f1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887189
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.a1', '8.c1.b1', '8.d1.b1', '12.f1.c1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1324, -1, 1098, -1, 265, -1, 167, -1], 'generators': [1, 38, 16, 48], 'label': '144.41.4.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.f1.c1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887190
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '216.111', 'aut_weyl_index': 4, 'centralizer': '36.a1.a1', 'complements': ['72.b1.b1', '72.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.f1.a1', '4.f1.b1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3234, 5172, 4337, 2576, 2065, 1011, 3143, 4720], 'generators': [1, 48, 2, 72, 16], 'label': '144.41.2.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'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887191
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.b1', '8.c1.b1', '8.d1.b1', '12.f1.d1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1324, -1, 305, -1, 265, -1, 587, -1], 'generators': [73, 38, 16, 48], 'label': '144.41.4.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.f1.d1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.d1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887192
    {'ambient': '144.41', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 54, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '18.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6752, 9155, 8794, 9209, 8533, 9141, 7935, 9383], 'generators': [2, 36, 48, 72], 'label': '144.41.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '72.17', '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': '8.5'}
  • id: 61887193
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 36, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.f1.a1', '12.f1.b1', '18.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4699, -1, 6119, -1, 3730, -1, 5539, -1], 'generators': [1, 2, 72, 48], 'label': '144.41.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '72.17', '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': '12.4'}
  • id: 61887194
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 36, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.c1.a1', '12.d1.b1', '12.f1.c1', '12.f1.d1', '18.b1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4699, -1, 5151, -1, 3730, -1, 4803, -1], 'generators': [1, 38, 72, 48], 'label': '144.41.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '72.17', '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': '12.4'}
  • id: 61887195
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.b1', '12.e1.a1', '18.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5845, -1, 7776, -1, 6001, -1, 8477, -1], 'generators': [53, 2, 72, 48], 'label': '144.41.6.c1.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.c1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61887196
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.d1.a1', '12.e1.a1', '18.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5845, -1, 7392, -1, 6001, -1, 6973, -1], 'generators': [53, 38, 72, 48], 'label': '144.41.6.c1.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.c1.b1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61887197
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1', '18.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7991, -1, 9362, -1, 6852, -1, 9015, -1], 'generators': [1, 36, 72, 48], 'label': '144.41.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61887198
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.d1.b1', '18.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8783, -1, 8156, -1, 7689, -1, 7402, -1], 'generators': [3, 36, 72, 48], 'label': '144.41.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61887199
    {'ambient': '144.41', 'aut_centralizer_order': 144, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 144, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2669, 3862, 3865, 4995, 2804, 4072, 3912, 3912], 'generators': [72, 112, 48], 'label': '144.41.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887200
    {'ambient': '144.41', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '18.a1.a1', 'complements': ['18.a1.a1', '18.e1.a1', '18.c1.a1', '18.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.a1', '4.f1.c1'], 'contains': ['16.a1.a1', '24.c1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1324, 2414, 1574, 2057, 474, 2079, 1082, 2782], 'generators': [1, 16, 48], 'label': '144.41.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '144.41', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887201
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '216.111', 'aut_weyl_index': 4, 'centralizer': '36.a1.b1', 'complements': ['72.b1.a1', '72.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.a1', '4.c1.b1', '4.f1.c1', '4.f1.d1', '6.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3234, 5172, 3543, 791, 2065, 1011, 2398, 2150], 'generators': [1, 48, 38, 72, 16], 'label': '144.41.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.a1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887202
    {'ambient': '144.41', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '18.a1.a1', 'complements': ['18.a1.a1', '18.e1.a1', '18.c1.a1', '18.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.b1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.c1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1324, 2414, 939, 1231, 474, 2079, 1422, 1425], 'generators': [73, 16, 48], 'label': '144.41.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '144.41', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887203
    {'ambient': '144.41', 'aut_centralizer_order': 36, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 144, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '24.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [248, -1, 3022, -1, 1609, -1, 2139, -1], 'generators': [2, 112, 48], 'label': '144.41.8.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': '144.41', '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: 61887204
    {'ambient': '144.41', 'aut_centralizer_order': 36, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 144, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.f1.c1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.b1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [248, -1, 447, -1, 1609, -1, 365, -1], 'generators': [38, 112, 48], 'label': '144.41.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.c1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887205
    {'ambient': '144.41', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '24.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [814, -1, 2016, -1, 1012, -1, 1761, -1], 'generators': [3, 16, 48], 'label': '144.41.8.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': '144.41', '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': '18.1'}
  • id: 61887206
    {'ambient': '144.41', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 16, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.f1.c1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [814, -1, 112, -1, 1012, -1, 743, -1], 'generators': [55, 16, 48], 'label': '144.41.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.d1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 61887207
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 54, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.c1.a1', '18.c1.b1', '18.d1.a1', '18.e1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9137, -1, 9888, -1, 9556, -1, 9656, -1], 'generators': [1, 2, 36], 'label': '144.41.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887208
    {'ambient': '144.41', 'aut_centralizer_order': 108, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4147, 6121, 6937, 7232, 4716, 5791, 6100, 6420], 'generators': [2, 72, 48], 'label': '144.41.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887209
    {'ambient': '144.41', 'aut_centralizer_order': 108, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.a1.a1', '6.b1.b1', '6.c1.b1'], 'contains': ['24.a1.a1', '24.b1.b1', '36.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4147, 6121, 5355, 5265, 4716, 5791, 4440, 7829], 'generators': [38, 72, 48], 'label': '144.41.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887210
    {'ambient': '144.41', 'aut_centralizer_order': 216, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '36.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7615, 8052, 8832, 8497, 6852, 7509, 7402, 5259], 'generators': [36, 48, 72], 'label': '144.41.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '72.17', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887211
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.b1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '36.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3411, -1, 4604, -1, 3402, -1, 4931, -1], 'generators': [1, 72, 48], 'label': '144.41.12.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887212
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '216.111', 'aut_weyl_index': 4, 'centralizer': '72.a1.a1', 'complements': ['72.b1.b1', '72.c1.a1', '72.c1.b1', '72.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.b1', '4.e1.a1', '6.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4572, 638, 6119, 6046, 3626, 4809, 5350, 6015], 'generators': [53, 48, 2, 72, 16], 'label': '144.41.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '72.17', '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': '72.17'}
  • id: 61887213
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.c1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '36.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4883, -1, 6302, -1, 3940, -1, 5270, -1], 'generators': [3, 72, 48], 'label': '144.41.12.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '72.17', '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': '12.4'}
  • id: 61887214
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.b1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.b1', '36.d1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4883, -1, 5985, -1, 3940, -1, 5610, -1], 'generators': [55, 72, 48], 'label': '144.41.12.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '72.17', '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': '12.4'}
  • id: 61887215
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.c1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '36.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6362, -1, 7697, -1, 6180, -1, 7826, -1], 'generators': [53, 72, 48], 'label': '144.41.12.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '72.17', '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': '12.4'}
  • id: 61887216
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.d1.a1', '36.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 3974, -1, 2207, -1, 3195, -1], 'generators': [1, 2, 48], 'label': '144.41.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887217
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.c1.b1', '24.d1.a1', '36.f1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 3110, -1, 2207, -1, 3535, -1], 'generators': [73, 2, 48], 'label': '144.41.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887218
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '6.b1.b1'], 'contains': ['24.b1.b1', '24.c1.a1', '24.d1.b1', '36.f1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 2329, -1, 2207, -1, 2516, -1], 'generators': [1, 38, 48], 'label': '144.41.12.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.f1.c1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887219
    {'ambient': '144.41', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '6.b1.b1'], 'contains': ['24.b1.b1', '24.c1.b1', '24.d1.b1', '36.f1.d1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 2028, -1, 2207, -1, 2855, -1], 'generators': [73, 38, 48], 'label': '144.41.12.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.f1.d1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887220
    {'ambient': '144.41', 'aut_centralizer_order': 144, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 144, 'centralizer': '2.c1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '8.d1.b1'], 'contains': ['48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [580, 3672, 521, 3571, 1609, 4072, 1592, 3352], 'generators': [112], 'label': '144.41.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '144.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887221
    {'ambient': '144.41', 'aut_centralizer_order': 108, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 108, 'centralizer': '4.b1.a1', 'complements': ['8.b1.a1', '8.b1.b1', '8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.a1.b1', '36.b1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7778, 9362, 9300, 8283, 9541, 8664, 8892, 8907], 'generators': [2, 36], 'label': '144.41.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['36.a1.a1', '36.a1.b1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.1', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887222
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.d1.a1', '36.f1.a1', '36.f1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6009, -1, 7212, -1, 5530, -1, 7001, -1], 'generators': [1, 2, 72], 'label': '144.41.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887223
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '216.111', 'aut_weyl_index': 4, 'centralizer': '72.a1.a1', 'complements': ['72.b1.a1', '72.c1.a1', '72.c1.b1', '72.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.c1.a1', '4.e1.a1', '6.c1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4572, 638, 5723, 3989, 3626, 4809, 3846, 6969], 'generators': [53, 48, 38, 72, 16], 'label': '144.41.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '72.17', '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': '72.17'}
  • id: 61887224
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '9.a1.a1'], 'contains': ['36.a1.b1', '36.c1.a1', '36.d1.b1', '36.f1.c1', '36.f1.d1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6009, -1, 5126, -1, 5530, -1, 6614, -1], 'generators': [1, 38, 72], 'label': '144.41.18.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.b1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887225
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.d1.b1', '36.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6971, -1, 8827, -1, 7450, -1, 9232, -1], 'generators': [53, 2], 'label': '144.41.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887226
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.a1.a1'], 'contains': ['36.a1.b1', '36.d1.a1', '36.e1.a1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6971, -1, 8035, -1, 7450, -1, 8213, -1], 'generators': [53, 38], 'label': '144.41.18.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887227
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.e1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8520, -1, 9733, -1, 8227, -1, 9722, -1], 'generators': [1, 36], 'label': '144.41.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887228
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 108, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.d1.a1', '36.d1.b1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9752, -1, 8411, -1, 9003, -1, 8553, -1], 'generators': [3, 36], 'label': '144.41.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61887229
    {'ambient': '144.41', 'aut_centralizer_order': 432, 'aut_label': '24.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.a1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4076, 5707, 5781, 6305, 4432, 5531, 5864, 5342], 'generators': [72, 48], 'label': '144.41.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887230
    {'ambient': '144.41', 'aut_centralizer_order': 108, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '72.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1458, -1, 4011, -1, 3282, -1, 3978, -1], 'generators': [2, 48], 'label': '144.41.24.b1.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.b1.a1', 'projective_image': '144.41', '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': '2.1'}
  • id: 61887231
    {'ambient': '144.41', 'aut_centralizer_order': 108, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.a1.b1', '12.f1.c1', '12.f1.d1'], 'contains': ['48.a1.a1', '72.b1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1458, -1, 1544, -1, 3282, -1, 2280, -1], 'generators': [38, 48], 'label': '144.41.24.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.b1.b1', 'projective_image': '144.41', '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': '2.1'}
  • id: 61887232
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.f1.a1', '12.f1.c1'], 'contains': ['48.a1.a1', '72.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1996, -1, 2780, -1, 2207, -1, 2959, -1], 'generators': [1, 48], 'label': '144.41.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '144.41', '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': '6.1'}
  • id: 61887233
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.f1.b1', '12.f1.d1'], 'contains': ['48.a1.a1', '72.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1996, -1, 1845, -1, 2207, -1, 3299, -1], 'generators': [73, 48], 'label': '144.41.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887234
    {'ambient': '144.41', 'aut_centralizer_order': 18, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.45', 'aut_weyl_index': 18, 'centralizer': '8.a1.a1', 'complements': ['72.c1.a1', '72.c1.b1', '72.d1.a1', '72.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.d1.a1', '6.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5385, 9258, 7008, 8894, 6173, 7754, 4808, 8161], 'generators': [2, 48, 36, 112, 72], 'label': '144.41.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.a1.b1', '4.d1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61887235
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '72.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2506, -1, 3201, -1, 2745, -1, 3638, -1], 'generators': [3, 48], 'label': '144.41.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '144.41', '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': '6.1'}
  • id: 61887236
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.d1.b1', '12.f1.c1', '12.f1.d1'], 'contains': ['48.a1.a1', '72.d1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2506, -1, 868, -1, 2745, -1, 2620, -1], 'generators': [55, 48], 'label': '144.41.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '24.d1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61887237
    {'ambient': '144.41', 'aut_centralizer_order': 216, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '2.a1.a1', 'complements': ['4.f1.c1', '4.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5272, 6742, 7492, 7537, 6232, 6643, 7774, 6886], 'generators': [2, 72], 'label': '144.41.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '18.a1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.1', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887238
    {'ambient': '144.41', 'aut_centralizer_order': 216, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '2.a1.b1', 'complements': ['4.f1.a1', '4.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.a1.a1', '18.b1.b1', '18.c1.b1'], 'contains': ['72.a1.a1', '72.b1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5272, 6742, 6741, 6181, 6232, 6643, 6227, 7829], 'generators': [38, 72], 'label': '144.41.36.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1.b1', 'normal_contained_in': ['12.a1.b1', '18.a1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.b1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.1', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887239
    {'ambient': '144.41', 'aut_centralizer_order': 432, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '2.d1.a1', 'complements': ['4.f1.a1', '4.f1.b1', '4.f1.c1', '4.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.a1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8584, 8069, 9303, 8407, 8227, 7754, 8345, 6088], 'generators': [36], 'label': '144.41.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.b1.a1', '18.a1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.1', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887240
    {'ambient': '144.41', 'aut_centralizer_order': 48, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.b1.a1', '18.b1.b1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.c1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5853, -1, 4875, -1, 5008, -1, 6614, -1], 'generators': [1, 72], 'label': '144.41.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887241
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.b1.a1', '18.c1.b1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6433, -1, 7083, -1, 5620, -1, 7001, -1], 'generators': [3, 72], 'label': '144.41.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887242
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '18.b1.b1', '18.c1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.d1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6433, -1, 6399, -1, 5620, -1, 7388, -1], 'generators': [55, 72], 'label': '144.41.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.b1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887243
    {'ambient': '144.41', 'aut_centralizer_order': 48, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.c1.a1', '18.c1.b1', '18.d1.a1'], 'contains': ['72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7643, -1, 8827, -1, 7129, -1, 8684, -1], 'generators': [53], 'label': '144.41.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '72.17', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887244
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.b1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': '36T135', 'count': 18, 'diagramx': [3787, -1, 5672, -1, 3857, -1, 5114, -1], 'generators': [1, 2], 'label': '144.41.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887245
    {'ambient': '144.41', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.111', 'aut_weyl_index': 4, 'centralizer': '36.b1.a1', 'complements': ['72.b1.a1', '72.b1.b1', '72.d1.a1', '72.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '6.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6356, 2621, 7580, 7345, 4485, 3148, 6114, 617], 'generators': [1, 48, 36, 72, 16], 'label': '144.41.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 61887246
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '18.b1.a1'], 'contains': ['72.b1.a1', '72.c1.b1', '72.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': '36T135', 'count': 18, 'diagramx': [3787, -1, 5217, -1, 3857, -1, 5501, -1], 'generators': [73, 2], 'label': '144.41.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887247
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.c1', '18.b1.b1'], 'contains': ['72.b1.b1', '72.c1.a1', '72.d1.b1'], 'core': '144.a1.a1', 'coset_action_label': '36T135', 'count': 18, 'diagramx': [3787, -1, 3477, -1, 3857, -1, 4341, -1], 'generators': [1, 38], 'label': '144.41.36.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.b1', 'old_label': '36.f1.c1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887248
    {'ambient': '144.41', 'aut_centralizer_order': 12, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.d1', '18.b1.b1'], 'contains': ['72.b1.b1', '72.c1.b1', '72.d1.b1'], 'core': '144.a1.a1', 'coset_action_label': '36T135', 'count': 18, 'diagramx': [3787, -1, 3134, -1, 3857, -1, 4728, -1], 'generators': [73, 38], 'label': '144.41.36.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.b1', 'old_label': '36.f1.d1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887249
    {'ambient': '144.41', 'aut_centralizer_order': 432, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.d1.b1'], 'contains': ['144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1904, 4759, 2021, 5503, 2767, 5531, 3299, 5342], 'generators': [48], 'label': '144.41.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '144.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.10', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61887250
    {'ambient': '144.41', 'aut_centralizer_order': 864, 'aut_label': '72.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.a1.a1', '36.a1.b1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.d1.b1', '36.e1.a1'], 'contains': ['144.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5853, 6104, 6741, 6859, 5620, 6599, 7001, 6088], 'generators': [72], 'label': '144.41.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '36.a1.a1', '36.a1.b1', '36.b1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '72.17', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.17', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887251
    {'ambient': '144.41', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.a1.a1', '36.f1.a1', '36.f1.b1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2852, -1, 5514, -1, 4395, -1, 5770, -1], 'generators': [2], 'label': '144.41.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887252
    {'ambient': '144.41', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '36.a1.b1', '36.f1.c1', '36.f1.d1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2852, -1, 3293, -1, 4395, -1, 4072, -1], 'generators': [38], 'label': '144.41.72.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '72.b1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887253
    {'ambient': '144.41', 'aut_centralizer_order': 48, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.c1.a1', '36.f1.a1', '36.f1.c1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3390, -1, 4316, -1, 3320, -1, 4751, -1], 'generators': [1], 'label': '144.41.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887254
    {'ambient': '144.41', 'aut_centralizer_order': 48, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '36.c1.a1', '36.f1.b1', '36.f1.d1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3390, -1, 4016, -1, 3320, -1, 5091, -1], 'generators': [73], 'label': '144.41.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.c1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887255
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.d1.a1', '36.f1.a1', '36.f1.b1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3899, -1, 5038, -1, 3857, -1, 5430, -1], 'generators': [3], 'label': '144.41.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887256
    {'ambient': '144.41', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 2, 'centralizer': '72.a1.a1', 'complements': ['72.b1.a1', '72.b1.b1', '72.c1.a1', '72.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1', '6.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7205, 7310, 6499, 5017, 5329, 6123, 4275, 3435], 'generators': [3, 48, 36, 72, 16], 'label': '144.41.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '72.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.17'}
  • id: 61887257
    {'ambient': '144.41', 'aut_centralizer_order': 24, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '36.d1.b1', '36.f1.c1', '36.f1.d1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3899, -1, 2977, -1, 3857, -1, 4412, -1], 'generators': [55], 'label': '144.41.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.b1', 'old_label': '72.d1.b1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887258
    {'ambient': '144.41', 'aut_centralizer_order': None, 'aut_label': '144.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', '72.a1.a1', '72.b1.a1', '72.b1.b1', '72.c1.a1', '72.c1.b1', '72.d1.a1', '72.d1.b1'], 'contains': [], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3390, 5499, 4166, 6373, 3857, 6050, 4921, 5715], 'generators': [], 'label': '144.41.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '72.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '144.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61887259
    {'ambient': '144.41', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 9, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.c1.b1', '6.d1.a1', '6.e1.a1', '9.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7827, -1, 7993, -1, 7196, -1, 7402, -1], 'generators': [1, 48, 2, 36, 72], 'label': '144.41.3.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': '72.17', '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': '24.14'}